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arXiv · 1309.7395

Median eigenvalues of bipartite subcubic graphs

Bojan Mohar
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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.

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Bojan Mohar. 2013-09-28. Median eigenvalues of bipartite subcubic graphs. https://doi.org/10.1017/s0963548316000201

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