Which digraphs with ring structure are essentially cyclic?

Advances in Applied Mathematics

Volumn 45, Issue 2, 2010, Pages 232-251

  Agaev, Rafig ^a   Chebotarev, Pavel ^a  

^a TRAPEZNIKOV INSTITUTE OF CONTROL SCIENCES   (Russian Federation)

Author keywords

Chebyshev polynomial; Directed graph; Essential cyclicity; Laplacian matrix; Laplacian spectrum; Spanning tree; Weighted digraph

Indexed keywords

CHEBYSHEV POLYNOMIALS; CYCLICITY; DIRECTED GRAPHS; LAPLACIAN MATRICES; LAPLACIAN SPECTRA; SPANNING TREE; WEIGHTED DIGRAPH;

LAPLACE TRANSFORMS; PARALLEL ARCHITECTURES; POLYNOMIALS; TELECOMMUNICATION NETWORKS; TREES (MATHEMATICS);

GRAPH THEORY;

EID: 77953680854     PISSN: 01968858     EISSN: 10902074     Source Type: Journal    
DOI: 10.1016/j.aam.2010.01.005     Document Type: Article

References (25)

1. R.P. Agaev, and P.Yu. Chebotarev The matrix of maximum out forests of a digraph and its applications Autom. Remote Control 61 2000 1424 1450
2. R.P. Agaev, and P.Yu. Chebotarev Spanning forests of a digraph and their applications Autom. Remote Control 62 2001 443 466
3. R. Agaev, and P. Chebotarev On the spectra of nonsymmetric Laplacian matrices Linear Algebra Appl. 399 2005 157 168
4. W.N. Anderson, and T.D. Morley Eigenvalues of the Laplacian of a graph Linear Multilinear Algebra 18 1985 141 145
5. F.T. Boesch, and H. Prodinger Spanning tree formulas and Chebyshev polynomials Graphs Combin. 2 1986 191 200
6. J.S. Caughman, and J.J.P. Veerman Kernels of directed graph Laplacians Electron. J. Combin. 13 1 2006 R39
7. P. Chebotarev Laplacian matrices and essentially cyclic weighted digraphs Abstracts of the 13th Conference of the International Linear Algebra Society 2006 Free University of Amsterdam 60 61
8. P. Chebotarev, and R. Agaev Forest matrices around the Laplacian matrix Linear Algebra Appl. 356 2002 253 274
9. P. Chebotarev, R. Agaev, When is the Laplacian spectrum of a weighted digraph real? in: International GAMM-SIAM Conference on Applied Linear Algebra, University of Düsseldorf, 2006, P. 29
10. P.Yu. Chebotarev, and R.P. Agaev Coordination in multiagent systems and Laplacian spectra of digraphs Autom. Remote Control 70 2009 469 483
11. P.Yu. Chebotarev, and E.V. Shamis The matrix-forest theorem and measuring relations in small social groups Autom. Remote Control 58 1997 1505 1514
12. P.Yu. Chebotarev, and E.V. Shamis On proximity measures for graph vertices Autom. Remote Control 59 1998 1443 1459
13. F. Chung Laplacians and the Cheeger inequality for directed graphs Ann. Comb. 9 2005 1 19
14. D.M. Cvetković, M. Doob, and H. Sachs Spectra of Graphs 1980 Academic Press New York
15. M. Fiedler Bounds for eigenvalues of doubly stochastic matrices Linear Algebra Appl. 5 1972 299 310
16. M. Fiedler, and J. Sedláek O W-basích orientovaných graf asopis Pst. Mat. 83 1958 214 225
17. F. Harary Graph Theory 1969 Addison-Wesley Reading, MA
18. M. Marcus, and H. Minc A Survey of Matrix Theory and Matrix Inequalities 1964 Allyn and Bacon Boston
19. R. Olfati-Saber, J.A. Fax, and R.M. Murray Consensus and cooperation in networked multi-agent systems Proc. IEEE 95 2007 215 233
20. S. Paszkowski Zastosowania Numeryczne Wielomianów i Szeregów Czebyszewa 1975 Państwowe Wydawnictwo Naukowe Warsaw
21. W. Ren, and R.W. Beard Distributed Consensus in Multi-Vehicle Cooperative Control 2008 Springer-Verlag London
22. G. Udrea Catalan's identity and Chebyshev polynomials of the second kind Port. Math. 52 1995 391 397
23. J.J.P. Veerman, G. Lafferriere, J.S. Caughman, and A. Wiiliams Flocks and formations J. Stat. Phys. 121 2005 901 936
24. Ch.W. Wu Algebraic connectivity of directed graphs Linear Multilinear Algebra 53 2005 203 223
25. Y. Zhang, X. Yong, and M. Golin Chebyshev polynomials and spanning tree formulas for circulant and related graphs Discrete Math. 298 2005 334 364