메뉴 건너뛰기




Volumn 402, Issue 1-3, 2005, Pages 207-227

On Rayleigh-Ritz ratios of a generalized Laplacian matrix of directed graphs

Author keywords

Connectivity; Directed graphs; Dynamical systems; Eigenvalues; Irreducible matrices; Laplacian matrix; Markov chains; Synchronization

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; GRAPH THEORY; INTEGRATION; MARKOV PROCESSES; MATHEMATICAL MODELS; MATRIX ALGEBRA; SET THEORY; SYNCHRONIZATION; THEOREM PROVING; TIME VARYING SYSTEMS;

EID: 17744377743     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2004.12.014     Document Type: Article
Times cited : (65)

References (26)
  • 1
  • 2
    • 0001350119 scopus 로고
    • Algebraic connectivity of graphs
    • M. Fiedler Algebraic connectivity of graphs Czechoslovak Math. J. 23 98 1973 298 305
    • (1973) Czechoslovak Math. J. , vol.23 , Issue.98 , pp. 298-305
    • Fiedler, M.1
  • 6
    • 0000004244 scopus 로고
    • A recurring theorem on determinants
    • O. Taussky A recurring theorem on determinants Amer. Math. Monthly 10 1949 672 676
    • (1949) Amer. Math. Monthly , vol.10 , pp. 672-676
    • Taussky, O.1
  • 8
    • 17744381357 scopus 로고    scopus 로고
    • On bounds of extremal eigenvalues of irreducible and m-reducible matrices
    • in press
    • C.W. Wu, On bounds of extremal eigenvalues of irreducible and m-reducible matrices, Linear Algebra Appl., in press (doi:10.1016/j.laa.2004.12.004)
    • Linear Algebra Appl.
    • Wu, W.1
  • 9
    • 0042158972 scopus 로고
    • Bounds for eigenvalues of doubly stochastic matrices
    • M. Fiedler Bounds for eigenvalues of doubly stochastic matrices Linear Algebra Appl. 5 1972 299 310
    • (1972) Linear Algebra Appl. , vol.5 , pp. 299-310
    • Fiedler, M.1
  • 10
    • 0000827674 scopus 로고
    • A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory
    • M. Fiedler A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory Czechoslovak Math. J. 25 100 1975 619 633
    • (1975) Czechoslovak Math. J. , vol.25 , Issue.100 , pp. 619-633
    • Fiedler, M.1
  • 11
    • 0035885345 scopus 로고    scopus 로고
    • Comparison of perturbation bounds for the stationary distribution of a Markov chain
    • G.E. Cho, and C.D. Meyer Comparison of perturbation bounds for the stationary distribution of a Markov chain Linear Algebra Appl. 335 2001 137 150
    • (2001) Linear Algebra Appl. , vol.335 , pp. 137-150
    • Cho, G.E.1    Meyer, C.D.2
  • 13
    • 0002676043 scopus 로고    scopus 로고
    • Some applications of Laplace eigenvalues of graphs
    • G. Hahn G. Sabidussi Kluwer
    • B. Mohar Some applications of Laplace eigenvalues of graphs G. Hahn G. Sabidussi Graph Symmetry: Algebraic Methods and Applications 1997 Kluwer 225 275
    • (1997) Graph Symmetry: Algebraic Methods and Applications , pp. 225-275
    • Mohar, B.1
  • 14
    • 0026925324 scopus 로고
    • New spectral methods for ratio cut partitioning and clustering
    • L. Hagen, and A.B. Kahng New spectral methods for ratio cut partitioning and clustering IEEE Trans. Comput.-Aided Design 11 9 1992 1074 1085
    • (1992) IEEE Trans. Comput.-Aided Design , vol.11 , Issue.9 , pp. 1074-1085
    • Hagen, L.1    Kahng, A.B.2
  • 15
    • 0001216057 scopus 로고
    • The Laplacian spectrum of graphs
    • Y. Alavi G. Chartrand O.R. Oellermann A.J. Schwenk Wiley
    • B. Mohar The Laplacian spectrum of graphs Y. Alavi G. Chartrand O.R. Oellermann A.J. Schwenk Graph Theory, Combinatorics, and Applications vol. 2 1991 Wiley 871 898
    • (1991) Graph Theory, Combinatorics, and Applications , vol.2 , pp. 871-898
    • Mohar, B.1
  • 16
    • 0001186333 scopus 로고
    • An upper bound on the diameter of a graph from eigenvalues associated with its Laplacian
    • F.R.K. Chung, V. Faber, and T.A. Manteuffel An upper bound on the diameter of a graph from eigenvalues associated with its Laplacian SIAM J. Discrete Math. 7 3 1994 443 457
    • (1994) SIAM J. Discrete Math. , vol.7 , Issue.3 , pp. 443-457
    • Chung, F.R.K.1    Faber, V.2    Manteuffel, T.A.3
  • 17
    • 0035481261 scopus 로고    scopus 로고
    • Synchronization in arrays of coupled nonlinear systems: Passivity, circle criterion and observer design
    • C.W. Wu Synchronization in arrays of coupled nonlinear systems: passivity, circle criterion and observer design IEEE Trans. Circuits Systems I 48 10 2001 1257 1261
    • (2001) IEEE Trans. Circuits Systems I , vol.48 , Issue.10 , pp. 1257-1261
    • Wu, C.W.1
  • 18
    • 38249011751 scopus 로고
    • Optimal linear labeling and eigenvalues of graphs
    • M. Juvan, and B. Mohar Optimal linear labeling and eigenvalues of graphs Discrete Appl. Math. 36 1992 153 168
    • (1992) Discrete Appl. Math. , vol.36 , pp. 153-168
    • Juvan, M.1    Mohar, B.2
  • 19
    • 84987593465 scopus 로고
    • Laplace eigenvalues and bandwidth-type invariants of graphs
    • M. Juvan, and B. Mohar Laplace eigenvalues and bandwidth-type invariants of graphs J. Graph Theory 17 1993 393 407
    • (1993) J. Graph Theory , vol.17 , pp. 393-407
    • Juvan, M.1    Mohar, B.2
  • 20
    • 0029358909 scopus 로고
    • Synchronization in an array of linearly coupled dynamical systems
    • C.W. Wu, and L.O. Chua Synchronization in an array of linearly coupled dynamical systems IEEE Trans. Circuits Systems I 42 8 1995 430 447
    • (1995) IEEE Trans. Circuits Systems I , vol.42 , Issue.8 , pp. 430-447
    • Wu, C.W.1    Chua, L.O.2
  • 21
    • 0029390407 scopus 로고
    • Application of Kronecker products to the analysis of systems with uniform linear coupling
    • C.W. Wu, and L.O. Chua Application of Kronecker products to the analysis of systems with uniform linear coupling IEEE Trans. Circuits Systems I 42 10 1995 775 778
    • (1995) IEEE Trans. Circuits Systems I , vol.42 , Issue.10 , pp. 775-778
    • Wu, C.W.1    Chua, L.O.2
  • 23
    • 0347533037 scopus 로고    scopus 로고
    • Perturbation of coupling matrices and its effect on the synchronizability in arrays of coupled chaotic circuits
    • C.W. Wu Perturbation of coupling matrices and its effect on the synchronizability in arrays of coupled chaotic circuits Phys. Lett. A 319 2003 495 503
    • (2003) Phys. Lett. A , vol.319 , pp. 495-503
    • Wu, C.W.1
  • 24
    • 0037301537 scopus 로고    scopus 로고
    • Synchronization in coupled arrays of chaotic oscillators with nonreciprocal coupling
    • C.W. Wu Synchronization in coupled arrays of chaotic oscillators with nonreciprocal coupling IEEE Trans. Circuits Systems I 50 2 2003 294 297
    • (2003) IEEE Trans. Circuits Systems I , vol.50 , Issue.2 , pp. 294-297
    • Wu, C.W.1
  • 25
    • 67649098898 scopus 로고    scopus 로고
    • On a matrix inequality and its application to the synchronization in coupled chaotic systems
    • IBM, submitted for publication
    • C.W. Wu, On a matrix inequality and its application to the synchronization in coupled chaotic systems, Research Report RC23155, IBM, submitted for publication
    • Research Report , vol.RC23155
    • Wu, C.W.1
  • 26
    • 22544454677 scopus 로고    scopus 로고
    • Synchronization in networks of nonlinear dynamical systems coupled via a directed graph
    • in press
    • C.W. Wu, Synchronization in networks of nonlinear dynamical systems coupled via a directed graph, Nonlinearity, in press
    • Nonlinearity
    • Wu, C.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.