Chebyshev polynomials and spanning tree formulas for circulant and related graphs

Discrete Mathematics

Volumn 298, Issue 1-3, 2005, Pages 334-364

  Zhang, Yuanping ^a   Yong, Xuerong ^b   Golin, Mordecai J ^c  

^a LANZHOU UNIVERSITY OF TECHNOLOGY   (China)

^b RUTGERS UNIVERSITY   (United States)

^c HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Chebyshev polynomials; Circulant graphs; Spanning trees

Indexed keywords

MATRIX ALGEBRA; POLYNOMIALS; THEOREM PROVING;

CHEBYSHEV POLYNOMIALS; CIRCULANT GRAPHS; MATRIX TREE THEOREM; SPANNING TREES;

GRAPH THEORY;

EID: 24144436020     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disc.2004.10.025     Document Type: Conference Paper

References (27)

1. G. Baron, H. Prodinger, R.F. Tichy, F.T. Boesch, and J.F. Wang The number of spanning trees in the square of a cycle Fibonacci Quart. 23.3 1985 258 264
2. S. Bedrosian The Fibonacci numbers via trigonometric expressions J. Franklin Inst. 295 1973 175 177
3. S.D. Bedrosian Formulas for the number of trees in a networks IEEE Trans. Circuit Theory CT-8 1961 363 364
4. S.D. Bedrosian Generating formulas for the number of trees in a graph J. Franklin Inst. 277 1964 313 326
5. S.D. Bedrosian Formulas for the number of trees in certain incomplete graphs J. Franklin Inst. 289 1970 67 69
6. S.D. Bedrosian Tree counting polynomials for labelled graphs J. Franklin Inst. 312 1981 417 430
7. N. Biggs Algebraic Graph Theory second ed. 1993 Cambridge University Press London
8. F.T. Boesch, and H. Prodinger Spanning tree formulas and Chebyshev polynomials Graph Combin. 2 1986 191 200
9. F.T. Boesch, J.F. Wang, A conjecture on the number of spanning trees in the square of a cycle, in: Notes from New York Graph Theory Day V, New York Academy Sciences, New York, 1982, pp. 16.
10. G. Chartrand, and L. Lesniak Graphs & Digraphs third ed. 1996 Chapman & Hall London
11. C.J. Colbourn The Combinatorics of Network Reliability 1987 Oxford University Press New York
12. D. Cvetkovič, M. Doob, and H. Sachs Spectra of Graphs: Theory and Applications third ed. 1995 Johann Ambrosius Barth Heidelberg
13. B. Gilbert, and W. Myrvold Maximizing spanning trees in almost complete graphs Networks 30 1997 97 104
14. M.J. Golin, Y. Zhang, Further applications of Chebyshev polynomials in the derivation of spanning tree formulas for circulant graphs, in: Mathematics and Computer Science II: Algorithms, Trees, Combinatorics and Probabilities, Proceedings of the International Colloquium on Mathematics and Computer Science, Versailles, France, September 16-19, Birkhäuser-Verlag, Basel, 2002, pp. 541-552.
15. Z.J. Huang, and X.M. Li A general method for finding the number of spanning trees of some types of composite graphs Acta Math. Sci. 15 3 1995 259 268 (Chinese)
16. A.K. Kel'mans, and V.M. Chelnokov A certain polynomial of a graph and graphs with an extremal number of trees J. Combin. Theory (B) 16 1974 197 214
17. G. Kirchhoff Über die Auflösung der Gleichungen auf, welche man bei der Untersuchung der linearen Verteilung galvanischer Ströme geführt wird Ann. Phys. Chem. 72 1847 497 508
18. D.J. Kleitman, and B. Golden Counting trees in a certain class of graphs Amer. Math. Monthly 82 1975 40 44
19. S.D. Nikolopoulos, and P. Rondogiannis On the number of spanning trees of multi-star related graph Inform. Process. Lett. 65 1998 183 188
20. P.V. O'Neil The number of spanning trees in a certain network Notices Amer. Math. Soc. 10 1963 569
21. P.V. O'Neil Enumeration of spanning trees in certain graphs IEEE Trans. Circuit Theory CT-17 1970 250
22. P.V. O'Neil, and P. Slepian The number of trees in a network IEEE Trans. Circuit Theory CT-13 1966 271 281
23. L. Weinberg Number of trees in graph Proc. IRE 46 1958 1954 1955
24. W.M. Yan, W. Myrvold, and K.L. Chung A formula for the number of spanning trees of a multi-star related graph Inform. Process. Lett. 68 1998 295 298
25. X. Yong, Talip, and Acenjian The numbers of spanning trees of the cubic cycle C N 3 and the quadruple cycle C N 4 Discrete Math. 169 1997 293 298
26. X. Yong, and F.J. Zhang A simple proof for the complexity of square cycle C p 2 J. Xinjiang Univ. 11 1994 12 16
27. Y.P. Zhang, X. Yong, and M.J. Golin The number of spanning trees in circulant graphs Discrete Math. 223 2000 337 350