A set <em>S ⊆ V (G)</em> is called a geodetic set if every vertex of <em>G</em> lies on a shortest <em>u-v</em> path for some <em>u, v ∈ S</em>, the minimum cardinality...A set <em>S ⊆ V (G)</em> is called a geodetic set if every vertex of <em>G</em> lies on a shortest <em>u-v</em> path for some <em>u, v ∈ S</em>, the minimum cardinality among all geodetic sets is called geodetic number and is denoted by <img src="Edit_82259359-0135-4a65-9378-b767f0405b48.png" alt="" />. A set <em>C ⊆ V (G)</em> is called a chromatic set if <em>C</em> contains all vertices of different colors in<em> G</em>, the minimum cardinality among all chromatic sets is called the chromatic number and is denoted by <img src="Edit_d849148d-5778-459b-abbb-ff25b5cd659b.png" alt="" />. A geo-chromatic set<em> S</em><sub><em>c</em></sub><em> ⊆ V (G</em><em>)</em> is both a geodetic set and a chromatic set. The geo-chromatic number <img src="Edit_505e203c-888c-471c-852d-4b9c2dd1a31c.png" alt="" /><em> </em>of<em> G</em> is the minimum cardinality among all geo-chromatic sets of<em> G</em>. In this paper, we determine the geodetic number and the geo-chromatic number of 2-cartesian product of some standard graphs like complete graphs, cycles and paths.展开更多
Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r ...Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.展开更多
The circular chromatic number of a graph is an important parameter of a graph. The distance graph G(Z,D) , with a distance set D , is the infinite graph with vertex set Z={0,±1,±2,...} in which tw...The circular chromatic number of a graph is an important parameter of a graph. The distance graph G(Z,D) , with a distance set D , is the infinite graph with vertex set Z={0,±1,±2,...} in which two vertices x and y are adjacent iff y-x∈D . This paper determines the circular chromatic numbers of two classes of distance graphs G(Z,D m,k,k+1 ) and G(Z,D m,k,k+1,k+2 ).展开更多
Metasurfaces are densely arrayed two⁃dimensional(2D)artificial planar metamaterials,which can manipulate the polarization,distribution,and amplitude of light by accurately controlling the phase of the scattering light...Metasurfaces are densely arrayed two⁃dimensional(2D)artificial planar metamaterials,which can manipulate the polarization,distribution,and amplitude of light by accurately controlling the phase of the scattering light.The flat metasurface has the potential to substantially reduce the thickness and complexity of the structures and allows ease of fabrication and integration into devices.However,the inherent chromatic aberration of the metasurface originating from the resonant dispersion of the antennas and the intrinsic chromatic dispersion limit their quality.How to effectively suppress or manipulate the chromatic aberration of metalenses has attracted worldwide attention in the last few years,leading to a variety of excellent achievements.Furthermore,utilizing the chromatic dispersion of metasurface to realize special functionalities is also of significant importance.In this review,the most promising recent examples of chromatic dispersion manipulation based on optical metasurface materials are highlighted and put into perspective.展开更多
For a general graph G, M（G） denotes its Mycielski graph. This article gives a number of new sufficient conditions for G to have the circular chromatic number xc（M（G）） equals to the chromatic number x（M（G））, ...For a general graph G, M（G） denotes its Mycielski graph. This article gives a number of new sufficient conditions for G to have the circular chromatic number xc（M（G）） equals to the chromatic number x（M（G））, which have improved some best sufficient conditions published up to date.展开更多
The edge-face chromatic number Xef （G） of a plane graph G is the least number of colors assigned to the edges and faces such that every adjacent or incident pair of them receives different colors. In this article, t...The edge-face chromatic number Xef （G） of a plane graph G is the least number of colors assigned to the edges and faces such that every adjacent or incident pair of them receives different colors. In this article, the authors prove that every 2-connected plane graph G with △（G）≥｜G｜ - 2≥9 has Xef（G） = △（G）.展开更多
By means of the chromatic polynomials, this paper provided a necessary and sufficient condition for the graph G being a mono-cycle graph（the Theorem 1）, a first class hi-cycle graph and a second class bicycle graph...By means of the chromatic polynomials, this paper provided a necessary and sufficient condition for the graph G being a mono-cycle graph（the Theorem 1）, a first class hi-cycle graph and a second class bicycle graph（the Theorem 2）, respectively.展开更多
A new regression algorithm of an adaptive reduced relevance vector machine is proposed to estimate the illumination chromaticity of an image for the purpose of color constancy. Within the framework of sparse Bayesian ...A new regression algorithm of an adaptive reduced relevance vector machine is proposed to estimate the illumination chromaticity of an image for the purpose of color constancy. Within the framework of sparse Bayesian learning, the algorithm extends the relevance vector machine by combining global and local kernels adaptively in the form of multiple kernels, and the improved locality preserving projection （LLP） is then applied to reduce the column dimension of the multiple kernel input matrix to achieve less training time. To estimate the illumination chromaticity, the algorithm is trained by fuzzy central values of chromaticity histograms of a set of images and the corresponding illuminants. Experiments with real images indicate that the proposed algorithm performs better than the support vector machine and the relevance vector machine while requiring less training time than the relevance vector machine.展开更多
Chromatic adaptation of human eyes to complex field is investigated using binocular asymmetric matching method. The results show that the leve of chromatic adapta- tion mainly depends on the average color of adapting ...Chromatic adaptation of human eyes to complex field is investigated using binocular asymmetric matching method. The results show that the leve of chromatic adapta- tion mainly depends on the average color of adapting field, whereas no obvious change oc- curs when the number of hues and their color differences vary in a complex field. The shifts of perceived color evoked by chromatic adaptation in CIE 1976 L U V color space are approximately proportional to the average color difference between the adapting field and reference field.展开更多
Effects of varieties on the content of tea pigment, L＊, a＊ and b＊ value of chromatic aberration of black tea infusion was studied. The correlation relationship between content of TF, TR, TB and L＊, a＊, b＊ value ...Effects of varieties on the content of tea pigment, L＊, a＊ and b＊ value of chromatic aberration of black tea infusion was studied. The correlation relationship between content of TF, TR, TB and L＊, a＊, b＊ value was extremely significant at P＆lt;0.05. Fresh tea leaves with plucking standard of 1 bud and 2 leaves could man-ufacture black tea with higher content of tea pigment, higher a＊ and b＊ value but lower L＊ value, than those of plucking standard of 1 bud and 3 leaves. But the discrepancy of certain parameter of the two plucking standards changed with vari-eties. Varieties’ quality potential could be concealed by improper plucking standards. Six varieties were divided into four groups on the basis of gross tea polyphenols in fresh tea leaves （GTP）, consumption of tea polyphenols to gross tea polyphenols ratio （CTP/GTP） and gross tea pigment to consumption of tea polyphenols ratio （GP/CTP）. Hybrid performed the very suitability of black tea manufacturing. To en-sure high quality of made black tea, suitable variety should be chosen and reason-able plucking standard also should be taken into consideration.展开更多
Adaptive mate choice has been accepted as the leading theory to explain the colorful plumage of birds.This theory hypothesizes that conspicuous colors act as signals to advertise the qualities of the owners.However,a ...Adaptive mate choice has been accepted as the leading theory to explain the colorful plumage of birds.This theory hypothesizes that conspicuous colors act as signals to advertise the qualities of the owners.However,a dilemma arises in that conspicuous colors may not only attract mates,but also alert predators.The"private channels of communication"hypothesis proposes that some intraspecific signals may not be visible to heterospecific animals because of different visual systems.To better understand the evolution of plumage colors and sexual selection in birds,here we studied the chromatic difference and achromatic differences of melanin-and carotenoid-based plumage coloration in five minivet species(Pericrocotus spp.)under conspecific and predator visual systems.We found that either the chromatic or achromatic difference among male or female minivets’plumage was consistently higher under conspecific vision than under predator vision for all five studied species of minivets.This result indicated that individual differences in plumage colors of minivets were visible to the conspecific receivers and hidden from potential predators as a result of evolution under predation risk and conspecific communication.However,males were under a higher risk of predation because they were more conspicuous than females to the vision of a nocturnal predator.展开更多
For a graph G,P(G,λ)denotes the chromatic polynomial of G.Two graphs G and H are said to be chromatically equivalent,denoted by G～H,if P(G,λ)=p(H,λ).Let [G]={H|H～G}.If [G]={G},then G is said to be chromaticall...For a graph G,P(G,λ)denotes the chromatic polynomial of G.Two graphs G and H are said to be chromatically equivalent,denoted by G～H,if P(G,λ)=p(H,λ).Let [G]={H|H～G}.If [G]={G},then G is said to be chromatically unique.For a complete 5 partite graph G with 5n vertices, define θ(G)=(α(G,6)-2 n+1 -2 n-1 + 5)/2 n-2 ,where α(G,6) denotes the number of 6 independent partition s of G.In this paper, the authors show that θ(G)≥0 and determine all g raphs with θ(G)=0,1,2,5/2,7/2,4,17/4.By using these results the chromaticity of 5 partite graphs of the form G-S with θ(G)=0,1,2,5/2,7/2,4,17/4 is inve stigated,where S is a set of edges of G.Many new chromatically unique 5 partite graphs are obtained.展开更多
The chromatically uniqueness of bipartite graphs K （m, n） - A（]A] = 2） was studied. With comparing the numbers of partitions into r color classes of two chromatically equivalent graphs, one general numerical condi...The chromatically uniqueness of bipartite graphs K （m, n） - A（]A] = 2） was studied. With comparing the numbers of partitions into r color classes of two chromatically equivalent graphs, one general numerical condition guaranteeing that K（ m, n） - A （ I A ] = 2） is chromatically unique were obtained. This covers and improves the former correlative results.展开更多
With its comprehensive application in network information engineering （e. g. dynamic spectrum allocation under different distance constraints ） and in network combination optimization （e. g. safe storage of deleter...With its comprehensive application in network information engineering （e. g. dynamic spectrum allocation under different distance constraints ） and in network combination optimization （e. g. safe storage of deleterious materials）, the graphs＇ cloring theory and chromatic uniqueness theory have been the forward position of graph theory research. The later concerns the equivalent classification of graphs with their color polynomials and the determination of uniqueness of some equivalent classification under isomorphism. In this paper, by introducing the concept of chromatic normality and comparing the number of partitions of two chromatically equivalent graphs, a general numerical condition guarenteeing that bipartite graphs K （ m, n） - A （A belong to E（K （m, n） ） and ｜ A ｜≥ 2） is chromatically unique was obtained and a lot of chromatic uniqueness graphs of bipartite graphs K（m, n） - A were determined. The results obtained in this paper were general. And the results cover and extend the majority of the relevant results obtained within the world.展开更多
For two integers k and d with （k, d） = 1 and k≥2d, let G^dk be the graph with vertex set {0,1,…k - 1 } in which ij is an edge if and only if d≤｜ i -j I｜≤k - d. The circular chromatic number χc（G） of a graph...For two integers k and d with （k, d） = 1 and k≥2d, let G^dk be the graph with vertex set {0,1,…k - 1 } in which ij is an edge if and only if d≤｜ i -j I｜≤k - d. The circular chromatic number χc（G） of a graph G is the minimum of k/d for which G admits a homomorphism to G^dk. The relationship between χc（ G- v） and χc （G）is investigated. In particular, the circular chromatic number of G^dk - v for any vertex v is determined. Some graphs withx χc（G - v） =χc（G） - 1 for any vertex v and with certain properties are presented. Some lower bounds for the circular chromatic number of a graph are studied, and a necessary and sufficient condition under which the circular chromatic number of a graph attains the lower bound χ- 1 ＋ 1/α is proved, where χ is the chromatic number of G and a is its independence number.展开更多
The circular chromatic number of a graph is a natural generalization of the chromatic number. Circular chromatic number contains more information about the structure of a graph than chromatic number does. In this pape...The circular chromatic number of a graph is a natural generalization of the chromatic number. Circular chromatic number contains more information about the structure of a graph than chromatic number does. In this paper we obtain the circular chromatic numbers of special graphs such as C t k and C t k-v, and give a simple proof of the circular chromatic number of H m,n .展开更多
Let G be a connected graph on n vertices with chromatic number k, and let ρ（G） be the distance signless Laplacian spectral radius of G. We show that ρ（G） ≥ 2n ＋ 2[n/k] - 4, with equality if and only if G is a...Let G be a connected graph on n vertices with chromatic number k, and let ρ（G） be the distance signless Laplacian spectral radius of G. We show that ρ（G） ≥ 2n ＋ 2[n/k] - 4, with equality if and only if G is a regular Turan graph.展开更多
文摘A set <em>S ⊆ V (G)</em> is called a geodetic set if every vertex of <em>G</em> lies on a shortest <em>u-v</em> path for some <em>u, v ∈ S</em>, the minimum cardinality among all geodetic sets is called geodetic number and is denoted by <img src="Edit_82259359-0135-4a65-9378-b767f0405b48.png" alt="" />. A set <em>C ⊆ V (G)</em> is called a chromatic set if <em>C</em> contains all vertices of different colors in<em> G</em>, the minimum cardinality among all chromatic sets is called the chromatic number and is denoted by <img src="Edit_d849148d-5778-459b-abbb-ff25b5cd659b.png" alt="" />. A geo-chromatic set<em> S</em><sub><em>c</em></sub><em> ⊆ V (G</em><em>)</em> is both a geodetic set and a chromatic set. The geo-chromatic number <img src="Edit_505e203c-888c-471c-852d-4b9c2dd1a31c.png" alt="" /><em> </em>of<em> G</em> is the minimum cardinality among all geo-chromatic sets of<em> G</em>. In this paper, we determine the geodetic number and the geo-chromatic number of 2-cartesian product of some standard graphs like complete graphs, cycles and paths.
文摘Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.
文摘The circular chromatic number of a graph is an important parameter of a graph. The distance graph G(Z,D) , with a distance set D , is the infinite graph with vertex set Z={0,±1,±2,...} in which two vertices x and y are adjacent iff y-x∈D . This paper determines the circular chromatic numbers of two classes of distance graphs G(Z,D m,k,k+1 ) and G(Z,D m,k,k+1,k+2 ).
基金National Program on Key Basic Research Project of China(Grant No.2017YFA0303700)the National Natural Science Foundation of China(Grant Nos.11621091,11822406,11774164,11834007 and 11774162)。
文摘Metasurfaces are densely arrayed two⁃dimensional(2D)artificial planar metamaterials,which can manipulate the polarization,distribution,and amplitude of light by accurately controlling the phase of the scattering light.The flat metasurface has the potential to substantially reduce the thickness and complexity of the structures and allows ease of fabrication and integration into devices.However,the inherent chromatic aberration of the metasurface originating from the resonant dispersion of the antennas and the intrinsic chromatic dispersion limit their quality.How to effectively suppress or manipulate the chromatic aberration of metalenses has attracted worldwide attention in the last few years,leading to a variety of excellent achievements.Furthermore,utilizing the chromatic dispersion of metasurface to realize special functionalities is also of significant importance.In this review,the most promising recent examples of chromatic dispersion manipulation based on optical metasurface materials are highlighted and put into perspective.
基金Supported by National Science Foundation of China (10371048)the Science Foundation of Three Gorges University.
文摘For a general graph G, M（G） denotes its Mycielski graph. This article gives a number of new sufficient conditions for G to have the circular chromatic number xc（M（G）） equals to the chromatic number x（M（G））, which have improved some best sufficient conditions published up to date.
基金This research is supported by NNSF of China(40301037, 10471131)
文摘The edge-face chromatic number Xef （G） of a plane graph G is the least number of colors assigned to the edges and faces such that every adjacent or incident pair of them receives different colors. In this article, the authors prove that every 2-connected plane graph G with △（G）≥｜G｜ - 2≥9 has Xef（G） = △（G）.
基金Supported by the NNSF of China(10861009)Supported by the Ministry of Education Science and Technology Item of China(206156)
文摘By means of the chromatic polynomials, this paper provided a necessary and sufficient condition for the graph G being a mono-cycle graph（the Theorem 1）, a first class hi-cycle graph and a second class bicycle graph（the Theorem 2）, respectively.
基金The National Natural Science Foundation of China(No60573139)the Innovation Foundation of Xidian University forGraduates (No05008)
文摘A new regression algorithm of an adaptive reduced relevance vector machine is proposed to estimate the illumination chromaticity of an image for the purpose of color constancy. Within the framework of sparse Bayesian learning, the algorithm extends the relevance vector machine by combining global and local kernels adaptively in the form of multiple kernels, and the improved locality preserving projection （LLP） is then applied to reduce the column dimension of the multiple kernel input matrix to achieve less training time. To estimate the illumination chromaticity, the algorithm is trained by fuzzy central values of chromaticity histograms of a set of images and the corresponding illuminants. Experiments with real images indicate that the proposed algorithm performs better than the support vector machine and the relevance vector machine while requiring less training time than the relevance vector machine.
文摘Chromatic adaptation of human eyes to complex field is investigated using binocular asymmetric matching method. The results show that the leve of chromatic adapta- tion mainly depends on the average color of adapting field, whereas no obvious change oc- curs when the number of hues and their color differences vary in a complex field. The shifts of perceived color evoked by chromatic adaptation in CIE 1976 L U V color space are approximately proportional to the average color difference between the adapting field and reference field.
基金Supported by Black Tea Team of Department of National Tea Industry and Technology System(CARS-23)Key Team of Department of Agriculture of Zhejiang Province(2011006)~~
文摘Effects of varieties on the content of tea pigment, L＊, a＊ and b＊ value of chromatic aberration of black tea infusion was studied. The correlation relationship between content of TF, TR, TB and L＊, a＊, b＊ value was extremely significant at P＆lt;0.05. Fresh tea leaves with plucking standard of 1 bud and 2 leaves could man-ufacture black tea with higher content of tea pigment, higher a＊ and b＊ value but lower L＊ value, than those of plucking standard of 1 bud and 3 leaves. But the discrepancy of certain parameter of the two plucking standards changed with vari-eties. Varieties’ quality potential could be concealed by improper plucking standards. Six varieties were divided into four groups on the basis of gross tea polyphenols in fresh tea leaves （GTP）, consumption of tea polyphenols to gross tea polyphenols ratio （CTP/GTP） and gross tea pigment to consumption of tea polyphenols ratio （GP/CTP）. Hybrid performed the very suitability of black tea manufacturing. To en-sure high quality of made black tea, suitable variety should be chosen and reason-able plucking standard also should be taken into consideration.
基金supported by the National Natural Science Foundation of China(32260127)the Education Department of Hainan Province(HnjgY2022-12)+1 种基金the Hainan Provincial Natural Science Foundation of China(320CXTD437)the Hainan Provincial Innovative Research Program for Graduates(Qhys2022-241)。
文摘Adaptive mate choice has been accepted as the leading theory to explain the colorful plumage of birds.This theory hypothesizes that conspicuous colors act as signals to advertise the qualities of the owners.However,a dilemma arises in that conspicuous colors may not only attract mates,but also alert predators.The"private channels of communication"hypothesis proposes that some intraspecific signals may not be visible to heterospecific animals because of different visual systems.To better understand the evolution of plumage colors and sexual selection in birds,here we studied the chromatic difference and achromatic differences of melanin-and carotenoid-based plumage coloration in five minivet species(Pericrocotus spp.)under conspecific and predator visual systems.We found that either the chromatic or achromatic difference among male or female minivets’plumage was consistently higher under conspecific vision than under predator vision for all five studied species of minivets.This result indicated that individual differences in plumage colors of minivets were visible to the conspecific receivers and hidden from potential predators as a result of evolution under predation risk and conspecific communication.However,males were under a higher risk of predation because they were more conspicuous than females to the vision of a nocturnal predator.
基金Supported by the National Natural Science Foundation of China (1 0 0 61 0 0 3) and the ScienceFoundation of the State Education Ministry of China
文摘For a graph G,P(G,λ)denotes the chromatic polynomial of G.Two graphs G and H are said to be chromatically equivalent,denoted by G～H,if P(G,λ)=p(H,λ).Let [G]={H|H～G}.If [G]={G},then G is said to be chromatically unique.For a complete 5 partite graph G with 5n vertices, define θ(G)=(α(G,6)-2 n+1 -2 n-1 + 5)/2 n-2 ,where α(G,6) denotes the number of 6 independent partition s of G.In this paper, the authors show that θ(G)≥0 and determine all g raphs with θ(G)=0,1,2,5/2,7/2,4,17/4.By using these results the chromaticity of 5 partite graphs of the form G-S with θ(G)=0,1,2,5/2,7/2,4,17/4 is inve stigated,where S is a set of edges of G.Many new chromatically unique 5 partite graphs are obtained.
基金Supported by the Natural Science Foundation of Jiangxi , China (No.0511006)
文摘The chromatically uniqueness of bipartite graphs K （m, n） - A（]A] = 2） was studied. With comparing the numbers of partitions into r color classes of two chromatically equivalent graphs, one general numerical condition guaranteeing that K（ m, n） - A （ I A ] = 2） is chromatically unique were obtained. This covers and improves the former correlative results.
基金Natural Science Foundation of Fujian, China (No.S0650011)
文摘With its comprehensive application in network information engineering （e. g. dynamic spectrum allocation under different distance constraints ） and in network combination optimization （e. g. safe storage of deleterious materials）, the graphs＇ cloring theory and chromatic uniqueness theory have been the forward position of graph theory research. The later concerns the equivalent classification of graphs with their color polynomials and the determination of uniqueness of some equivalent classification under isomorphism. In this paper, by introducing the concept of chromatic normality and comparing the number of partitions of two chromatically equivalent graphs, a general numerical condition guarenteeing that bipartite graphs K （ m, n） - A （A belong to E（K （m, n） ） and ｜ A ｜≥ 2） is chromatically unique was obtained and a lot of chromatic uniqueness graphs of bipartite graphs K（m, n） - A were determined. The results obtained in this paper were general. And the results cover and extend the majority of the relevant results obtained within the world.
基金The National Natural Science Foundation of China(No.10671033)
文摘For two integers k and d with （k, d） = 1 and k≥2d, let G^dk be the graph with vertex set {0,1,…k - 1 } in which ij is an edge if and only if d≤｜ i -j I｜≤k - d. The circular chromatic number χc（G） of a graph G is the minimum of k/d for which G admits a homomorphism to G^dk. The relationship between χc（ G- v） and χc （G）is investigated. In particular, the circular chromatic number of G^dk - v for any vertex v is determined. Some graphs withx χc（G - v） =χc（G） - 1 for any vertex v and with certain properties are presented. Some lower bounds for the circular chromatic number of a graph are studied, and a necessary and sufficient condition under which the circular chromatic number of a graph attains the lower bound χ- 1 ＋ 1/α is proved, where χ is the chromatic number of G and a is its independence number.
文摘The circular chromatic number of a graph is a natural generalization of the chromatic number. Circular chromatic number contains more information about the structure of a graph than chromatic number does. In this paper we obtain the circular chromatic numbers of special graphs such as C t k and C t k-v, and give a simple proof of the circular chromatic number of H m,n .
基金Supported by National Natural Science Foundation of China(Grant Nos.1107100211371028)+4 种基金Program for New Century Excellent Talents in University(Grant No.NCET-10-0001)Key Project of Chinese Ministry of Education(Grant No.210091)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20103401110002)Natural Science Research Foundation of Department of Education of Anhui Province(Grant No.KJ2013A196)Scientific Research Fund for Fostering Distinguished Young Scholars of Anhui University(Grant No.KJJQ1001)
文摘Let G be a connected graph on n vertices with chromatic number k, and let ρ（G） be the distance signless Laplacian spectral radius of G. We show that ρ（G） ≥ 2n ＋ 2[n/k] - 4, with equality if and only if G is a regular Turan graph.
