The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. We say a graph G is star extremal if its circular chromatic number is equal to its...The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. We say a graph G is star extremal if its circular chromatic number is equal to its fractional chromatic number. This paper gives an improvement of a theorem. And we show that several classes of circulant graphs are star extremal.展开更多
The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. A graph is called star extremal if its fractional chromatic number equals to its c...The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. A graph is called star extremal if its fractional chromatic number equals to its circular chromatic number (also known as the star chromatic number). This paper studies the star extremality of the circulant graphs whose generating sets are of the form {±1,±k} .展开更多
In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind...In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k (r 1,r 2,…,r k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.展开更多
Two new design approaches for constructing Low-Density Parity-Check(LDPC) codes are proposed.One is used to design regular Quasi-Cyclic LDPC(QC-LDPC) codes with girth at least 8.The other is used to design irregular L...Two new design approaches for constructing Low-Density Parity-Check(LDPC) codes are proposed.One is used to design regular Quasi-Cyclic LDPC(QC-LDPC) codes with girth at least 8.The other is used to design irregular LDPC codes.Both of their parity-check matrices are composed of Circulant Permutation Matrices(CPMs).When iteratively decoded with the Sum-Product Algorithm(SPA),these proposed codes exhibit good performances over the AWGN channel.展开更多
In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of th...In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.展开更多
The popularly used circulant matrix model of deconvolution is mostly heavily ill-posed or singular and it is not suitable to many blind deconvolution problems. The aperiodic matrix model can improve the condition numb...The popularly used circulant matrix model of deconvolution is mostly heavily ill-posed or singular and it is not suitable to many blind deconvolution problems. The aperiodic matrix model can improve the condition number of deconvolution problems and its accommodation is much wider than the circulant one's. This paper discusses a comparison of the two models including their ill-posedness, the rationality of the approximation by the models, and their computational efficiency. The comparison shows that the aperiodic model is promising in the development of new restoration algorithms.展开更多
A graph is called an integral graph if it has an integral spectrum i.e.,all eigenvalues are integers.A graph is called circulant graph if it is Cayley graph on the circulant group,i.e.,its adjacency matrix is circulan...A graph is called an integral graph if it has an integral spectrum i.e.,all eigenvalues are integers.A graph is called circulant graph if it is Cayley graph on the circulant group,i.e.,its adjacency matrix is circulant.The rank of a graph is defined to be the rank of its adjacency matrix.This importance of the rank,due to applications in physics,chemistry and combinatorics.In this paper,using Ramanujan sums,we study the rank of integral circulant graphs and gave some simple computational formulas for the rank and provide an example which shows the formula is sharp.展开更多
The preconditioned generalized minimal residual(GMRES) method is a common method for solving non-symmetric,large and sparse linear systems which originated in discrete ordinary differential equations by Boundary value...The preconditioned generalized minimal residual(GMRES) method is a common method for solving non-symmetric,large and sparse linear systems which originated in discrete ordinary differential equations by Boundary value methods.In this paper,we propose a new circulant preconditioner to speed up the convergence rate of the GMRES method, which is a convex linear combination of P-circulant and Strang-type circulant preconditioners. Theoretical and practical arguments are given to show that this preconditioner is feasible and effective in some cases.展开更多
Denote by C n(S) the circulant digraph with vertex set Z n={0,1,2,...,n-1} and symbol set S(≠-S)Z n }. Let X be the automorphism group of C n(S) and X 0 the stabilizer of 0 in X. Then C n(S) is arc ...Denote by C n(S) the circulant digraph with vertex set Z n={0,1,2,...,n-1} and symbol set S(≠-S)Z n }. Let X be the automorphism group of C n(S) and X 0 the stabilizer of 0 in X. Then C n(S) is arc transitive if and only if X 0 acts transitively on S. In this paper, C n(S) with X 0| S being the symmetric group is characterized by its symbol set. By the way all the arc transitive circulant digraphs of degree 2 and 3 are given.展开更多
The decentralized stabilization of continuous and discrete linear large scale systems with symmetric circulant structure was studied.A few sufficient conditions on decentralized stabilization of such systems were prop...The decentralized stabilization of continuous and discrete linear large scale systems with symmetric circulant structure was studied.A few sufficient conditions on decentralized stabilization of such systems were proposed.For the continuous systems,by introducing a concept called the magnitude of interconnected structure,a very important property that the decentralized stabilization of such systems is fully determined by the structure of each isolated subsystem that is obtained when the magnitude of interconnected structure of the overall system is given.So the decentralized stabilization of such systems can be got by only appropriately designing or modifying the structure of each isolated subsystem,no matter how complicated the interconnected structure of the overall system is.A algorithm for obtaining decentralized state feedback to stabilize the overall system is given.The discrete systems were also discussed.The results show that there is a great dfference on decentralized stabilization between continuous case and discrete case.展开更多
In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine theisomorphic classes of circulant digraphs of degree 3. In particul...In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine theisomorphic classes of circulant digraphs of degree 3. In particular, we characterizethose circulant digraphs of degree 3 which don't satisfy Adam's conjecture.展开更多
Let Gn（C） be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc（Jr~） the set of all primitive matrices in Gn（C）. In this paper, some necessary and sufficient condi...Let Gn（C） be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc（Jr~） the set of all primitive matrices in Gn（C）. In this paper, some necessary and sufficient conditions for A in the semigroup Gn（C） to be primitive are given. We also show that Gc（Jn） is a subsemigroup of Gn（C）.展开更多
In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some propert...In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some properties of the idempotent elements of the semigroup of generalized circulant Fuzzy matrixes in connection with minimum cycle of row vector.展开更多
For a connected graph G, the distance energy of G is a recently developed energytype invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix G. A graph is called circulant if it is C...For a connected graph G, the distance energy of G is a recently developed energytype invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix G. A graph is called circulant if it is Cayley graph on the circulant group, i.e., its adjacency matrix is circulant. In this note, we establish lower bounds for the distance energy of circulant graphs. In particular, we discuss upper bound of distance energy for the 4-circulant graph.展开更多
Symmetric circulant matrices (or shortly symmetric circulants) are a very special class of matrices sometimes arising in problems of discrete periodic convolutions with symmetric kernel. First, we collect major proper...Symmetric circulant matrices (or shortly symmetric circulants) are a very special class of matrices sometimes arising in problems of discrete periodic convolutions with symmetric kernel. First, we collect major properties of symmetric circulants scattered through the literature. Second, we report two new applications of these matrices to isotropic Markov chain models and electrical impedance tomography on a homogeneous disk with equidistant electrodes. A new special function is introduced for computation of the Ohm’s matrix. The latter application is illustrated with estimation of the resistivity of gelatin using an electrical impedance tomography setup.展开更多
We construct Hamilton cycles in connected loopless circulant digraphs of outdegree three with connection set of the form for an integer satisfying the condition for some integer such that , where . This extends work o...We construct Hamilton cycles in connected loopless circulant digraphs of outdegree three with connection set of the form for an integer satisfying the condition for some integer such that , where . This extends work of Miklavi and ?parl, who previously deter-mined the Hamiltonicity of these digraphs in the case where and , to other values of which depend on the generators and .展开更多
An L(h,k)-labeling of a graph G is an assignment of non-negative integers to the vertices such that if two vertices u and v are adjacent then they receive labels that differ by at least h, and when u and v are not adj...An L(h,k)-labeling of a graph G is an assignment of non-negative integers to the vertices such that if two vertices u and v are adjacent then they receive labels that differ by at least h, and when u and v are not adjacent but there is a two-hop path between them, then they receive labels that differ by at least k. The span λ of such a labeling is the difference between the largest and the smallest vertex labels assigned. Let λ<sub>h</sub>k</sup> ( G )denote the least λ such that G admits an L(h,k) -labeling using labels from {0,1,...λ}. A Cayley graph of group is called circulant graph of order n, if the group is isomorphic to Z<sub>n.</sub> In this paper, initially we investigate the L(h,k) -labeling for circulant graphs with “large” connection sets, and then we extend our observation and find the span of L(h,k) -labeling for any circulants of order n. .展开更多
文摘The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. We say a graph G is star extremal if its circular chromatic number is equal to its fractional chromatic number. This paper gives an improvement of a theorem. And we show that several classes of circulant graphs are star extremal.
文摘The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. A graph is called star extremal if its fractional chromatic number equals to its circular chromatic number (also known as the star chromatic number). This paper studies the star extremality of the circulant graphs whose generating sets are of the form {±1,±k} .
基金Supported by the National Natural Science Foundation of China(2 0 0 0 CG0 1 0 3) the Fund of"The Developing Program for Outstanding Person"in NPUS & T Innovation Foundation for Young Teachers of Northwestern Polytechnical University.
文摘In this paper, the spectrum and characteristic polynomial for a special kind of symmetric block circulant matrices are given.
文摘In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k (r 1,r 2,…,r k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.
基金Supported by the National Natural Science Foundation of China(Nos.61271199,61172022)
文摘Two new design approaches for constructing Low-Density Parity-Check(LDPC) codes are proposed.One is used to design regular Quasi-Cyclic LDPC(QC-LDPC) codes with girth at least 8.The other is used to design irregular LDPC codes.Both of their parity-check matrices are composed of Circulant Permutation Matrices(CPMs).When iteratively decoded with the Sum-Product Algorithm(SPA),these proposed codes exhibit good performances over the AWGN channel.
文摘In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.
文摘The popularly used circulant matrix model of deconvolution is mostly heavily ill-posed or singular and it is not suitable to many blind deconvolution problems. The aperiodic matrix model can improve the condition number of deconvolution problems and its accommodation is much wider than the circulant one's. This paper discusses a comparison of the two models including their ill-posedness, the rationality of the approximation by the models, and their computational efficiency. The comparison shows that the aperiodic model is promising in the development of new restoration algorithms.
基金Foundation item： Supported by Hunan Provincial Natural Science Foundation（13JJ3118）
文摘A graph is called an integral graph if it has an integral spectrum i.e.,all eigenvalues are integers.A graph is called circulant graph if it is Cayley graph on the circulant group,i.e.,its adjacency matrix is circulant.The rank of a graph is defined to be the rank of its adjacency matrix.This importance of the rank,due to applications in physics,chemistry and combinatorics.In this paper,using Ramanujan sums,we study the rank of integral circulant graphs and gave some simple computational formulas for the rank and provide an example which shows the formula is sharp.
基金Supported by the Scientific Research Foundation for Advisor Program of Higher Education of Gansu Province(1009-6)Supported by the Scientific Research Foundation for Youth Scholars of Hexi University(qn201015)
文摘The preconditioned generalized minimal residual(GMRES) method is a common method for solving non-symmetric,large and sparse linear systems which originated in discrete ordinary differential equations by Boundary value methods.In this paper,we propose a new circulant preconditioner to speed up the convergence rate of the GMRES method, which is a convex linear combination of P-circulant and Strang-type circulant preconditioners. Theoretical and practical arguments are given to show that this preconditioner is feasible and effective in some cases.
文摘Denote by C n(S) the circulant digraph with vertex set Z n={0,1,2,...,n-1} and symbol set S(≠-S)Z n }. Let X be the automorphism group of C n(S) and X 0 the stabilizer of 0 in X. Then C n(S) is arc transitive if and only if X 0 acts transitively on S. In this paper, C n(S) with X 0| S being the symmetric group is characterized by its symbol set. By the way all the arc transitive circulant digraphs of degree 2 and 3 are given.
文摘The decentralized stabilization of continuous and discrete linear large scale systems with symmetric circulant structure was studied.A few sufficient conditions on decentralized stabilization of such systems were proposed.For the continuous systems,by introducing a concept called the magnitude of interconnected structure,a very important property that the decentralized stabilization of such systems is fully determined by the structure of each isolated subsystem that is obtained when the magnitude of interconnected structure of the overall system is given.So the decentralized stabilization of such systems can be got by only appropriately designing or modifying the structure of each isolated subsystem,no matter how complicated the interconnected structure of the overall system is.A algorithm for obtaining decentralized state feedback to stabilize the overall system is given.The discrete systems were also discussed.The results show that there is a great dfference on decentralized stabilization between continuous case and discrete case.
基金Supported by the National Natural Science Foundation of China.
文摘In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine theisomorphic classes of circulant digraphs of degree 3. In particular, we characterizethose circulant digraphs of degree 3 which don't satisfy Adam's conjecture.
基金Supported by the National Natural Science Foundation of China(11071272,11101087)the Postdoctoral Science Foundation of China(2013M531785)+1 种基金the Natural Science Foundation of Fujian Province(2013J05006)the Foundation of Fuzhou University(2012-XQ-30)
文摘Let Gn（C） be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc（Jr~） the set of all primitive matrices in Gn（C）. In this paper, some necessary and sufficient conditions for A in the semigroup Gn（C） to be primitive are given. We also show that Gc（Jn） is a subsemigroup of Gn（C）.
文摘In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some properties of the idempotent elements of the semigroup of generalized circulant Fuzzy matrixes in connection with minimum cycle of row vector.
基金Project Supported by Scientific Research Fund of Hunan Provincial Education Department(15C1235)
文摘For a connected graph G, the distance energy of G is a recently developed energytype invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix G. A graph is called circulant if it is Cayley graph on the circulant group, i.e., its adjacency matrix is circulant. In this note, we establish lower bounds for the distance energy of circulant graphs. In particular, we discuss upper bound of distance energy for the 4-circulant graph.
文摘Symmetric circulant matrices (or shortly symmetric circulants) are a very special class of matrices sometimes arising in problems of discrete periodic convolutions with symmetric kernel. First, we collect major properties of symmetric circulants scattered through the literature. Second, we report two new applications of these matrices to isotropic Markov chain models and electrical impedance tomography on a homogeneous disk with equidistant electrodes. A new special function is introduced for computation of the Ohm’s matrix. The latter application is illustrated with estimation of the resistivity of gelatin using an electrical impedance tomography setup.
文摘We construct Hamilton cycles in connected loopless circulant digraphs of outdegree three with connection set of the form for an integer satisfying the condition for some integer such that , where . This extends work of Miklavi and ?parl, who previously deter-mined the Hamiltonicity of these digraphs in the case where and , to other values of which depend on the generators and .
文摘An L(h,k)-labeling of a graph G is an assignment of non-negative integers to the vertices such that if two vertices u and v are adjacent then they receive labels that differ by at least h, and when u and v are not adjacent but there is a two-hop path between them, then they receive labels that differ by at least k. The span λ of such a labeling is the difference between the largest and the smallest vertex labels assigned. Let λ<sub>h</sub>k</sup> ( G )denote the least λ such that G admits an L(h,k) -labeling using labels from {0,1,...λ}. A Cayley graph of group is called circulant graph of order n, if the group is isomorphic to Z<sub>n.</sub> In this paper, initially we investigate the L(h,k) -labeling for circulant graphs with “large” connection sets, and then we extend our observation and find the span of L(h,k) -labeling for any circulants of order n. .
