Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-30T15:17:38.341Z Has data issue: false hasContentIssue false

On the index of tricyclic Hamiltonian graphs

Published online by Cambridge University Press:  20 January 2009

F. K. Bell
Affiliation:
Department of Mathematics, University of Stirling, Stirling FK9 4LA, Scotland
P. Rowlinson
Affiliation:
Department of Mathematics, University of Stirling, Stirling FK9 4LA, Scotland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Among the tricyclic Hamiltonian graphs with a prescribed number of vertices, the unique graph with maximal index is determined. Some subsidiary results are also included.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

REFERENCES

1.Cvetković, D., Doob, M. and Sachs, H., Spectra of Graphs (Academic Press, New York, 1980).Google Scholar
2.Cvetković, D. and Rowlinson, P., Spectra of unicyclic graphs, Graphs Combin. 3 (1987), 723.CrossRefGoogle Scholar
3.Cvetković, D. and Rowlinson, P., On connected graphs with maximal index, Publ. Inst. Math. Beograd 44 (58) (1988), 2934.Google Scholar
4.Gantmacher, F. R., Theory of Matrices, Vol. II (Chelsea, New York, 1960).Google Scholar
5.Hoffman, A. J. and Smith, J. H., On the spectral radii of topologically equivalent graphs, Recent Advances in Graph Theory (ed. Fiedler, M., Academia Prague, 1975), 273281.Google Scholar
6.Rowlinson, P., A deletion-contraction algorithm for the characteristic polynomial of a multigraph, Proc. Royal Soc. Edinburgh 105A (1987), 153160.CrossRefGoogle Scholar
7.Rowlinson, P., On the maximal index of graphs with a prescribed number of edges, Linear Algebra Appl. 110 (1988), 4353.CrossRefGoogle Scholar
8.Schwenk, A. J., Computing the characteristic polynomial of a graph, Graphs and Combinatorics, Lecture Notes in Mathematics 406 (eds Bari, R. A. and Harary, F., Springer, New York, 1974), 153172.CrossRefGoogle Scholar
9.Simi, S. K.ć and Kocić, V. Lj., On the largest eigenvalue of some homeomorphic graphs, Publ. Inst. Math. Beograd 40 (54) (1986), 39.Google Scholar
10.Simić, S. K., On the largest eigenvalue of unicyclic graphs, Publ. Inst. Math. Beograd 42 (56) (1987), 1319.Google Scholar
11.Simić, S. K., Some results on the largest eigenvalue of a graph, Ars Combin. 24A (1987), 211219.Google Scholar
12.Simić, S. K., On the largest eigenvalue of bicylic graphs, to appear.Google Scholar