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Median Eigenvalues of Bipartite Subcubic Graphs

Part of: Graph theory

Published online by Cambridge University Press:  21 June 2016

BOJAN MOHAR
BOJAN MOHAR*
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada (e-mail: [email protected])
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Abstract

It is proved that the median eigenvalues of every connected bipartite graph G of maximum degree at most three belong to the interval [−1, 1] with a single exception of the Heawood graph, whose median eigenvalues are $\pm\sqrt{2}$. Moreover, if G is not isomorphic to the Heawood graph, then a positive fraction of its median eigenvalues lie in the interval [−1, 1]. This surprising result has been motivated by the problem about HOMO-LUMO separation that arises in mathematical chemistry.

MSC classification

Primary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 25 , Issue 5 , September 2016 , pp. 768 - 790
Copyright
Copyright © Cambridge University Press 2016 

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References

[1] Gutman, I. and Polanski, O. E. (1986) Mathematical Concepts in Organic Chemistry, Springer.Google Scholar
[2] Fowler, P. W. and Pisanski, T. (2010) HOMO-LUMO maps for fullerenes. Acta Chim. Slov. 57 513–517.Google Scholar
[3] Fowler, P. W. and Pisanski, T. (2010) HOMO-LUMO maps for chemical graphs. MATCH Commun. Math. Comput. Chem. 64 373–390.Google Scholar
[4] Godsil, C. and Royle, G. (2001) Algebraic Graph Theory, Springer.CrossRefGoogle Scholar
[5] Jaklič, G., Fowler, P. W. and Pisanski, T. (2012) HL-index of a graph. Ars Math. Contemp. 5 99–105.Google Scholar
[6] Mohar, B. (2013) Median eigenvalues of bipartite planar graphs. MATCH Commun. Math. Comput. Chem. 70 79–84.Google Scholar
[7] Mohar, B. (2015) Median eigenvalues and the HOMO-LUMO index of graphs. J. Combin. Theory Ser. B 112 78–92.Google Scholar