Median eigenvalues and the HOMO-LUMO index of graphs
Combinatorics
2014-01-10 v1
Abstract
Motivated by the problem about HOMO-LUMO separation that arises in mathematical chemistry, Fowler and Pisanski introduced the notion of the HL-index which measures how large in absolute value may be the median eigenvalues of a graph. In this note we provide rather tight lower and upper bounds on the maximum value of the HL-index among all graphs with given average degree. In particular, we determine the exact value of this parameter when restricted to chemically relevant graphs, i.e.\ graphs of maximum degree , and thus answer a question of Fowler and Pisanski. The proof provides additional insight about eigenvalue distribution of large subcubic graphs.
Keywords
Cite
@article{arxiv.1401.1865,
title = {Median eigenvalues and the HOMO-LUMO index of graphs},
author = {Bojan Mohar},
journal= {arXiv preprint arXiv:1401.1865},
year = {2014}
}
Comments
Submitted in September 2012