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arxiv: 1309.7395 · v1 · pith:KNV6GWZWnew · submitted 2013-09-28 · 🧮 math.CO

Median eigenvalues of bipartite subcubic graphs

classification 🧮 math.CO
keywords eigenvaluesmediangraphbipartiteheawoodintervalarisesbeen
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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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