Median eigenvalues of bipartite subcubic graphs
read the original 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.
This paper has not been read by Pith yet.
Forward citations
Cited by 2 Pith papers
-
Subcubic graphs without eigenvalues in $(-1, 1)$
Connected subcubic graphs without eigenvalues in (-1,1) consist of exactly two infinite families and seven sporadic graphs on at most 18 vertices.
-
Free-Fermion Subsystem Codes
Constructs free-fermion subsystem codes with a 2D topological example, graph-based solvability algorithm, and gap analysis via skew energy and median eigenvalues.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.