A function f： V（ G）→{1,1} defined on the vertices of a graph G is a signed total dominating function （STDF） if the sum of its function values over any open neighborhood is at least one. An STDF f is minimal if t...A function f： V（ G）→{1,1} defined on the vertices of a graph G is a signed total dominating function （STDF） if the sum of its function values over any open neighborhood is at least one. An STDF f is minimal if there does not extst a STDF g： V（G）→{-1,1}, f≠g, for which g （ v ）≤f（ v ） for every v∈V（ G ）. The weight of a STDF is the sum of its function values over all vertices. The signed total domination number of G is the minimum weight of a STDF of G, while the upper signed domination number of G is the maximum weight of a minimal STDF of G, In this paper, we present sharp upper bounds on the upper signed total domination number of a nearly regular graph.展开更多
Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs（SRGs） with parameters（N, k, λ, μ） achieves full quantum speedup. The problem is reconsidered ...Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs（SRGs） with parameters（N, k, λ, μ） achieves full quantum speedup. The problem is reconsidered in terms of scattering quantum walk, a type of discrete-time quantum walks. Here, the search space is confined to a low-dimensional subspace corresponding to the collapsed graph of SRGs. To quantify the algorithm＇s performance, we leverage the fundamental pairing theorem, a general theory developed by Cottrell for quantum search of structural anomalies in star graphs.The search algorithm on the SRGs with k scales as N satisfies the theorem, and results can be immediately obtained, while search on the SRGs with k scales as√N does not satisfy the theorem, and matrix perturbation theory is used to provide an analysis. Both these cases can be solved in O（√N） time steps with a success probability close to 1. The analytical conclusions are verified by simulation results on two SRGs. These examples show that the formalism on star graphs can be applied more generally.展开更多
Let G be a graph of order n and μ be an adjacency eigenvalue of G with multiplicity k ≥ 1. A star complement H for μ in G is an induced subgraph of G with n-k vertices and no eigenvalue μ, and the vertex subset X ...Let G be a graph of order n and μ be an adjacency eigenvalue of G with multiplicity k ≥ 1. A star complement H for μ in G is an induced subgraph of G with n-k vertices and no eigenvalue μ, and the vertex subset X = V(G-H) is called a star set for μ in G. The star complement technique provides a spectral tool for reconstructing a certain part of a graph from the remaining part. In this paper, we study the regular graphs with K_(t,s)(s ≥ t ≥ 2) as a star complement for an eigenvalue μ, especially, characterize the case of t = 3 completely, obtain some properties when t = s, and propose some problems for further study.展开更多
In this paper, we construct some families of strongly regular graphs on finite fields by using unions of cyclotomic classes and index 2 Gauss sums. New infinite families of strongly regular graphs are found.
The goal of the present paper is to provide a gallery of small directed strongly regular graphs.For each graph of order n≤12 and valency k<n/2,a diagram is depicted,its relation to other small directed strongly re...The goal of the present paper is to provide a gallery of small directed strongly regular graphs.For each graph of order n≤12 and valency k<n/2,a diagram is depicted,its relation to other small directed strongly regular graphs is revealed,the full group of automorphisms is described,and some other nice properties are given.To each graph a list of interesting subgraphs is provided as well.展开更多
A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number, denoted τ c (G), is the minimum cardinality of a clique-transversal set in G. In th...A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number, denoted τ c (G), is the minimum cardinality of a clique-transversal set in G. In this paper we present the bounds on the clique-transversal number for regular graphs and characterize the extremal graphs achieving the lower bound. Also, we give the sharp bounds on the clique-transversal number for claw-free cubic graphs and we characterize the extremal graphs achieving the lower bound.展开更多
An(s,t)-partition of a graph G=(V,E)is a partition of V=V 1∪V 2 suchthatδ(G[V_(1)])≥s andδ(G[V_(2)])≥t.Ithasbeenconjecturedthat,forsufficiently large n,every d-regular graph of order n has a(d/2,d/2)-partition(ca...An(s,t)-partition of a graph G=(V,E)is a partition of V=V 1∪V 2 suchthatδ(G[V_(1)])≥s andδ(G[V_(2)])≥t.Ithasbeenconjecturedthat,forsufficiently large n,every d-regular graph of order n has a(d/2,d/2)-partition(called an internal partition).Inthispaper,weprovethateveryd-regulargraphofordern hasa(d/2,d/2)partition(called a weak internal partition)for d≤9 and sufficiently large n.展开更多
A generalized strongly regular graphof grade p,as anew generalization of strongly regular graphs,is a regular graph such that the number of common neighbours of both any two adjacent vertices and any two non-adjacent ...A generalized strongly regular graphof grade p,as anew generalization of strongly regular graphs,is a regular graph such that the number of common neighbours of both any two adjacent vertices and any two non-adjacent vertices takes on p distinct values.For any vertex u of a generalized strongly regular graph of grade 2 with parameters(n,k;a_(1),a_(2);c_(1),c_(2)),if the number of the vertices that are adjacent to u and share ai(i=1,2)common neighbours with u,or are non-adjacent to u and share c,(i=1,2)common neighbours with is independent of the choice of the vertex u,then the generalized strongly regular graph of grade 2 is free.In this paper,we investigate the generalized strongly regular graph of grade 2 with parameters(n,k;k-1,a_(2);k-1,c_(2))and provide the sufficient and necessary conditions for the existence of a family of free generalized strongly regular graphs of grade 2.展开更多
The ferry problem may be viewed as generalizations of the classical wolf-goatcabbage puzzle. The ferry cover problem is to determine the minimum required boat capacity to safely transport n items represented by a conf...The ferry problem may be viewed as generalizations of the classical wolf-goatcabbage puzzle. The ferry cover problem is to determine the minimum required boat capacity to safely transport n items represented by a conflict graph. The Alcuin number of a conflict graph is the smallest capacity of a boat for which the graph possesses a feasible ferry schedule. In this paper the authors determine the Alcuin number of regular graphs and graphs with maximum degree at most five.展开更多
Fault diagnosis is an important area of study with regard to the design and maintenance of multiprocessor systems.A new measure for fault diagnosis of systems,namely,non-inclusive diagnosability(denoted by MM^(*)),was...Fault diagnosis is an important area of study with regard to the design and maintenance of multiprocessor systems.A new measure for fault diagnosis of systems,namely,non-inclusive diagnosability(denoted by MM^(*)),was proposed by Ding et al.In this paper,we establish the non-inclusive diagnosability of a class of regular graphs under the PMC model and the MM^(*)model.As applications,the non-inclusive diagnosabilities of hypercubes,hierarchical hypercubes,folded hypercubes,star graphs,bubble-sort graphs,pancake graphs and dual cubes are determined under the PMC model and the[Math Processing Error]model.展开更多
Plesnik in 1972 proved that an （m - 1）-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m - 1 edges. Alder et al. in 1999 showed that...Plesnik in 1972 proved that an （m - 1）-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m - 1 edges. Alder et al. in 1999 showed that if G is a regular （2n ＋ 1）-edge-connected bipartite graph, then G has a 1-factor containing any given edge and excluding any given matching of size n. In this paper we obtain some sufficient conditions related to the edge-connectivity for an n-regular graph to have a k-factor containing a set of edges and （or） excluding a set of edges, where 1 ≤ k ≤n/2. In particular, we generalize Plesnik＇s result and the results obtained by Liu et al. in 1998, and improve Katerinis＇ result obtained 1993. Furthermore, we show that the results in this paper are the best possible.展开更多
For any even integer k and any integer i, we prove that a （kr ＋i）-regular multigraph contains a k-factor if it contains no more than kr - 3k/2＋ i ＋ 2 cut edges, and this result is the best possible to guarantee t...For any even integer k and any integer i, we prove that a （kr ＋i）-regular multigraph contains a k-factor if it contains no more than kr - 3k/2＋ i ＋ 2 cut edges, and this result is the best possible to guarantee the existence of k-factor in terms of the number of cut edges. We further give a characterization for k-factor free regular graphs.展开更多
A graph G is k-covered if each edge of G belongs to a k-factor of G. We determine some valuee of k for which every r-regular graph with edge-connectivity λ is k-covered.
Let G = （V, E） be a finite, simple and undirected graph with p vertices and q edges. An （a, d）-vertex-antimagic total labeling of G is a bijection f from V（G） t2 E（G） onto the set of consecutive integers 1, 2,...Let G = （V, E） be a finite, simple and undirected graph with p vertices and q edges. An （a, d）-vertex-antimagic total labeling of G is a bijection f from V（G） t2 E（G） onto the set of consecutive integers 1, 2,... ,p ＋ q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f（x） assigned to the vertex x together with all values f（xy） assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1,..., r ＋ 1.展开更多
Koetzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongLy-regular self- complementary graph whose order is 4k ＋ 1, where 4k ＋ 1 ...Koetzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongLy-regular self- complementary graph whose order is 4k ＋ 1, where 4k ＋ 1 = x^2 ＋ y^2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k ＋ 1 orders.展开更多
Let Гt-（G） be upper minus total domination number of G. In this paper, We establish an upper bound of the upper minus total domination number of a regular graph G and characterize the extremal graphs attaining the ...Let Гt-（G） be upper minus total domination number of G. In this paper, We establish an upper bound of the upper minus total domination number of a regular graph G and characterize the extremal graphs attaining the bound. Thus, we answer an open problem by Yan, Yang and Shan展开更多
The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular...The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular graphs under some conditions do have an ascending subgraph decomposition.展开更多
Owing to the constraints of depth sensing technology,images acquired by depth cameras are inevitably mixed with various noises.For depth maps presented in gray values,this research proposes a novel denoising model,ter...Owing to the constraints of depth sensing technology,images acquired by depth cameras are inevitably mixed with various noises.For depth maps presented in gray values,this research proposes a novel denoising model,termed graph-based transform(GBT)and dual graph Laplacian regularization(DGLR)(DGLR-GBT).This model specifically aims to remove Gaussian white noise by capitalizing on the nonlocal self-similarity(NSS)and the piecewise smoothness properties intrinsic to depth maps.Within the group sparse coding(GSC)framework,a combination of GBT and DGLR is implemented.Firstly,within each group,the graph is constructed by using estimates of the true values of the averaged blocks instead of the observations.Secondly,the graph Laplacian regular terms are constructed based on rows and columns of similar block groups,respectively.Lastly,the solution is obtained effectively by combining the alternating direction multiplication method(ADMM)with the weighted thresholding method within the domain of GBT.展开更多
A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inne...A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.展开更多
We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility c...We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.展开更多
文摘A function f： V（ G）→{1,1} defined on the vertices of a graph G is a signed total dominating function （STDF） if the sum of its function values over any open neighborhood is at least one. An STDF f is minimal if there does not extst a STDF g： V（G）→{-1,1}, f≠g, for which g （ v ）≤f（ v ） for every v∈V（ G ）. The weight of a STDF is the sum of its function values over all vertices. The signed total domination number of G is the minimum weight of a STDF of G, while the upper signed domination number of G is the maximum weight of a minimal STDF of G, In this paper, we present sharp upper bounds on the upper signed total domination number of a nearly regular graph.
基金supported by the National Natural Science Foundation of China(Grant Nos.61502101 and 61170321)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20140651)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20110092110024)
文摘Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs（SRGs） with parameters（N, k, λ, μ） achieves full quantum speedup. The problem is reconsidered in terms of scattering quantum walk, a type of discrete-time quantum walks. Here, the search space is confined to a low-dimensional subspace corresponding to the collapsed graph of SRGs. To quantify the algorithm＇s performance, we leverage the fundamental pairing theorem, a general theory developed by Cottrell for quantum search of structural anomalies in star graphs.The search algorithm on the SRGs with k scales as N satisfies the theorem, and results can be immediately obtained, while search on the SRGs with k scales as√N does not satisfy the theorem, and matrix perturbation theory is used to provide an analysis. Both these cases can be solved in O（√N） time steps with a success probability close to 1. The analytical conclusions are verified by simulation results on two SRGs. These examples show that the formalism on star graphs can be applied more generally.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 1197118012271337)+1 种基金the Characteristic Innovation Project of General Colleges and Universities in Guangdong Province (Grant No. 2022KTSCX225)the Guangdong Education and Scientific Research Project (Grant No. 2021GXJK159)。
文摘Let G be a graph of order n and μ be an adjacency eigenvalue of G with multiplicity k ≥ 1. A star complement H for μ in G is an induced subgraph of G with n-k vertices and no eigenvalue μ, and the vertex subset X = V(G-H) is called a star set for μ in G. The star complement technique provides a spectral tool for reconstructing a certain part of a graph from the remaining part. In this paper, we study the regular graphs with K_(t,s)(s ≥ t ≥ 2) as a star complement for an eigenvalue μ, especially, characterize the case of t = 3 completely, obtain some properties when t = s, and propose some problems for further study.
基金supported by National Natural Science Foundation of China (Grant Nos.10971250 and 11171150)
文摘In this paper, we construct some families of strongly regular graphs on finite fields by using unions of cyclotomic classes and index 2 Gauss sums. New infinite families of strongly regular graphs are found.
文摘The goal of the present paper is to provide a gallery of small directed strongly regular graphs.For each graph of order n≤12 and valency k<n/2,a diagram is depicted,its relation to other small directed strongly regular graphs is revealed,the full group of automorphisms is described,and some other nice properties are given.To each graph a list of interesting subgraphs is provided as well.
基金the National Nature Science Foundation of China (Grant Nos.10571117,60773078)the Hong Kong Polytechnic University (Grant No.G-YX69) Shuguang Plan of Shanghai Education Development Foundation (Grant No.06SG42)
文摘A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number, denoted τ c (G), is the minimum cardinality of a clique-transversal set in G. In this paper we present the bounds on the clique-transversal number for regular graphs and characterize the extremal graphs achieving the lower bound. Also, we give the sharp bounds on the clique-transversal number for claw-free cubic graphs and we characterize the extremal graphs achieving the lower bound.
基金supported by NNSF of China(No.11671376)the Fundamental Research Funds for the Central Universities.
文摘An(s,t)-partition of a graph G=(V,E)is a partition of V=V 1∪V 2 suchthatδ(G[V_(1)])≥s andδ(G[V_(2)])≥t.Ithasbeenconjecturedthat,forsufficiently large n,every d-regular graph of order n has a(d/2,d/2)-partition(called an internal partition).Inthispaper,weprovethateveryd-regulargraphofordern hasa(d/2,d/2)partition(called a weak internal partition)for d≤9 and sufficiently large n.
基金supported by National Natural Science Foundation of China(No.11571091)Natural Science Foundation of Hebei Province,China(No.F2019205147)Innovation Program of Hebei Normal University,China(No.CXZZSS2020050).
文摘A generalized strongly regular graphof grade p,as anew generalization of strongly regular graphs,is a regular graph such that the number of common neighbours of both any two adjacent vertices and any two non-adjacent vertices takes on p distinct values.For any vertex u of a generalized strongly regular graph of grade 2 with parameters(n,k;a_(1),a_(2);c_(1),c_(2)),if the number of the vertices that are adjacent to u and share ai(i=1,2)common neighbours with u,or are non-adjacent to u and share c,(i=1,2)common neighbours with is independent of the choice of the vertex u,then the generalized strongly regular graph of grade 2 is free.In this paper,we investigate the generalized strongly regular graph of grade 2 with parameters(n,k;k-1,a_(2);k-1,c_(2))and provide the sufficient and necessary conditions for the existence of a family of free generalized strongly regular graphs of grade 2.
基金supported by the National Natural Science Foundation of China(Nos.11871329,11571222)
文摘The ferry problem may be viewed as generalizations of the classical wolf-goatcabbage puzzle. The ferry cover problem is to determine the minimum required boat capacity to safely transport n items represented by a conflict graph. The Alcuin number of a conflict graph is the smallest capacity of a boat for which the graph possesses a feasible ferry schedule. In this paper the authors determine the Alcuin number of regular graphs and graphs with maximum degree at most five.
基金supported by the National Natural Science Foundation of China(No.11571044)the Natural Science Foundation of Shanxi Province(No.201901D211106)。
文摘Fault diagnosis is an important area of study with regard to the design and maintenance of multiprocessor systems.A new measure for fault diagnosis of systems,namely,non-inclusive diagnosability(denoted by MM^(*)),was proposed by Ding et al.In this paper,we establish the non-inclusive diagnosability of a class of regular graphs under the PMC model and the MM^(*)model.As applications,the non-inclusive diagnosabilities of hypercubes,hierarchical hypercubes,folded hypercubes,star graphs,bubble-sort graphs,pancake graphs and dual cubes are determined under the PMC model and the[Math Processing Error]model.
基金FRGHong Kong Baptist University NSFC (60673047)SRFDP (20040422004) of China
文摘Plesnik in 1972 proved that an （m - 1）-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m - 1 edges. Alder et al. in 1999 showed that if G is a regular （2n ＋ 1）-edge-connected bipartite graph, then G has a 1-factor containing any given edge and excluding any given matching of size n. In this paper we obtain some sufficient conditions related to the edge-connectivity for an n-regular graph to have a k-factor containing a set of edges and （or） excluding a set of edges, where 1 ≤ k ≤n/2. In particular, we generalize Plesnik＇s result and the results obtained by Liu et al. in 1998, and improve Katerinis＇ result obtained 1993. Furthermore, we show that the results in this paper are the best possible.
基金Supported by Natural Sciences and Engineering Research Council of CanadaNNSF (Grant No. 10871119)RSDP (Grant No. 200804220001) of China
文摘For any even integer k and any integer i, we prove that a （kr ＋i）-regular multigraph contains a k-factor if it contains no more than kr - 3k/2＋ i ＋ 2 cut edges, and this result is the best possible to guarantee the existence of k-factor in terms of the number of cut edges. We further give a characterization for k-factor free regular graphs.
文摘A graph G is k-covered if each edge of G belongs to a k-factor of G. We determine some valuee of k for which every r-regular graph with edge-connectivity λ is k-covered.
基金Supported by Slovak VEGA Grant 1/0130/12Higher Education Commission Pakistan (Grant No.HEC(FD)/2007/555)the Ministry of Education of the Czech Republic (Grant No. MSM6198910027)
文摘Let G = （V, E） be a finite, simple and undirected graph with p vertices and q edges. An （a, d）-vertex-antimagic total labeling of G is a bijection f from V（G） t2 E（G） onto the set of consecutive integers 1, 2,... ,p ＋ q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f（x） assigned to the vertex x together with all values f（xy） assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1,..., r ＋ 1.
文摘Koetzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongLy-regular self- complementary graph whose order is 4k ＋ 1, where 4k ＋ 1 = x^2 ＋ y^2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k ＋ 1 orders.
基金Supported by the National Natural Science Foundation of China(No.61170302)Innovation Project of Optimization and Control of Network Systems of Zhejiang Normal University(ZSDZZZZXK03)
文摘Let Гt-（G） be upper minus total domination number of G. In this paper, We establish an upper bound of the upper minus total domination number of a regular graph G and characterize the extremal graphs attaining the bound. Thus, we answer an open problem by Yan, Yang and Shan
文摘The definition of the ascending subgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular graphs under some conditions do have an ascending subgraph decomposition.
基金National Natural Science Foundation of China(No.62372100)。
文摘Owing to the constraints of depth sensing technology,images acquired by depth cameras are inevitably mixed with various noises.For depth maps presented in gray values,this research proposes a novel denoising model,termed graph-based transform(GBT)and dual graph Laplacian regularization(DGLR)(DGLR-GBT).This model specifically aims to remove Gaussian white noise by capitalizing on the nonlocal self-similarity(NSS)and the piecewise smoothness properties intrinsic to depth maps.Within the group sparse coding(GSC)framework,a combination of GBT and DGLR is implemented.Firstly,within each group,the graph is constructed by using estimates of the true values of the averaged blocks instead of the observations.Secondly,the graph Laplacian regular terms are constructed based on rows and columns of similar block groups,respectively.Lastly,the solution is obtained effectively by combining the alternating direction multiplication method(ADMM)with the weighted thresholding method within the domain of GBT.
基金The National Natural Science Foundation of China (No.61362001,61102043,61262084,20132BAB211030,20122BAB211015)the Basic Research Program of Shenzhen(No.JC201104220219A)
文摘A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.
基金supported by the European Regional Development Fund through the program COMPETEby the Portuguese Government through the FCT—Fundacao para a Ciencia e a Tecnologia under the project PEst—C/MAT/UI0144/2013+1 种基金partially supported by Portuguese Funds trough CIDMA—Center for Research and development in Mathematics and Applications,Department of Mathematics,University of Aveiro,3810-193,Aveiro,Portugalthe Portuguese Foundation for Science and Technology(FCT-Fundacao para a Ciencia e Tecnologia),within Project PEst-OE/MAT/UI4106/2014
文摘We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.
