Maximizing spanning trees in almost complete graphs

Networks

Volumn 30, Issue 2, 1997, Pages 97-104

  Gilbert, Bryan ^a   Myrvold, Wendy ^a  

^a UNIVERSITY OF VICTORIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041194628     PISSN: 00283045     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0037(199709)30:2<97::AID-NET4>3.0.CO;2-F     Document Type: Article

References (30)

1. F. T. Boesch, On unreliability polynomials and graph connectivity in reliable network synthesis. J. Graph Theory 10(3) (1986) 339-352.
2. F. T. Boesch, X. Li, and C. Suffel, On the existence of uniformly optimally reliable networks. Networks 21 (1991) 181-194.
3. F. T. Boesch and C. L. Suffel, A survey of the algebraic approach to the study of spanning trees. Unpublished report (1984).
4. J. A. Bondy and U. S. R. Murty, Graph Theory with Applications. North-Holland, New York (1980).
5. R. A. Brualdi and H. J. Ryser, Combinatorial Matrix Theory. Cambridge University Press, New York (1991).
6. C.-S. Cheng, Optimality of certain asymmetrical experimental designs. Ann. Stat. 6 (1978) 1239-1261.
7. C.-S. Cheng, Maximizing the total number of spanning trees in a graph; two related problems in graph theory and optimum design theory. J. Comb. Theory, Ser. B 31 (1981) 240-248.
8. C. J. Colbourn, The Combinatorics of Network Reliability. Oxford University Press, New York (1987).
9. D. M. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs. Academic Press, New York (1980).
10. A. Gibbons, Algorithmic Graph Theory. Cambridge University Press, Cambridge (1989).
11. B. Gilbert, Maximizing spanning trees in almost complete graphs. Master's Thesis, Department of Computer Science, University of Victoria, Victoria, BC (1995).
12. A. K. Kel'mans, The number of trees in a graph. I. Automat. Remote Control (Translated from Avtomatika i Telemekhanika [(in Russian]) 26(12) (1965) 2194-2204.
13. A. K. Kel'mans, The number of trees in a graph. I. Automat. Remote Control (Translated from Avtomatika i Telemekhanika [(in Russian]) 26(12) (1965) 2194-2204.
14. A. K. Kel'mans, The number of trees in a graph, II. Automat. Remote Control (translated from Avtomatika i Telemekhanika [in Russian]) 27(2) (1966) 56-65.
15. A. K. Kel'mans, The number of trees in a graph, II. Automat. Remote Control (translated from Avtomatika i Telemekhanika [in Russian]) 27(2) (1966) 56-65.
16. A. K. Kel'mans, Comparison of graphs by their number of spanning trees. Discr. Math. 16(3) (1976) 241-261.
17. A. K. Kel'mans, Graphs with an extremal number of spanning trees: A research announcement. J. Graph Theory 4 (1980) 119-122.
18. A. K. Kel'mans, On graphs with randomly deleted edges. Acta Math. Acad. Sci. Hung. 37(1-3) (1981) 77-88.
19. A. K. Kel'mans and V. M. Chelnokov, A certain polynomial of a graph and graphs with an extremal number of trees. J. Comb. Theory, Ser. B 16 (1974) 197-214.
20. G. Kirchhoff, Über die Ausflösung der Gleichungen auf welche man bei der Untersuchungen der Linearen Verteilung Galvanisher Ströme geführt wird. Poggendorf Ann. Phys. 72 (1847) 497-508.
21. J. W. Moon, Enumerating labelled trees. Graph Theory and Theoretical Physics. (F. Harary, Ed.). Academic Press, New York (1967) 261-272.
22. W. Myrvold, K. H. Cheung, L. B. Page, and J. E. Perry, Uniformly-most reliable networks do not always exist. Networks 21 (1991) 417-419.
23. L. Petingi, On the Characterization of Graphs with Maximum Number of Spanning Trees. PhD Thesis, Stevens Institute of Technology, Hoboken, NJ (1991).
24. L. Petingi, F. Boesch, and C. Suffel, On the characterization of graphs with maximum number of spanning trees. Discr. Math., to appear.
25. A. Satyanarayana, L. Schoppmann, and C. L. Suffel, A reliability-improving graph transformation with applications to network reliability. Networks 22 (1992) 209-216.
26. D. R. Shier, Maximizing the number of spanning trees in a graph with n nodes and m edges. J. Res. Natl. Bur. Stand., Sect. B 78 (1974) 193-196.
27. H. N. V. Temperley, On the mutual cancellation of cluster integrals in Mayer's fugacity series. Proceed. Phys. Soc. 83 (1964) 3-16.
28. S. S. Tseng and L. R. Wang, Maximizing the number of spanning trees of networks based on cycle basis representation. Int. J. Comput. Math. 28 (1989) 47-56.
29. G. Wang, A proof of Boesch's conjecture. Networks 24 (1994) 277-284.
30. J. F. Wang and M. H. Wu, Network reliability analysis: On maximizing the number of spanning trees. Proceed. Natl. Sci. Council, Rep. China, Part A, Phys. Sci. Eng. 11 (3) (1987) 193-196.