Median eigenvalues of bipartite subcubic graphs

摘要

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 asingle exception of the Heawood graph, whose median eigenvalues are$\pm\sqrt{2}$. Moreover, if $G$ is not isomorphic to the Heawood graph, then apositive fraction of its median eigenvalues lie in the interval $[-1,1]$. Thissurprising result has been motivated by the problem about HOMO-LUMO separationthat arises in mathematical chemistry.