Graphs with Integer Matching Polynomial Roots
Combinatorics
2017-02-07 v3 Discrete Mathematics
Abstract
In this paper, we study graphs whose matching polynomial have only integer zeros. A graph is matching integral if the zeros of its matching polynomial are all integers. We characterize all matching integral traceable graphs.. We show that apart from K7 n (E(C3) [ E(C4)) there is no connected k-regular matching integral graph if k ? 2. It is also shown that if G is a graph with a perfect matching, then its matching polynomial has a zero in the interval (0, 1]. Finally, we describe all claw-free matching integral graphs.
Keywords
Cite
@article{arxiv.1608.00782,
title = {Graphs with Integer Matching Polynomial Roots},
author = {S. Akbari and P. Csikvari and A. Ghafari and S. Khalashi Ghezelahmad and M. Nahvi},
journal= {arXiv preprint arXiv:1608.00782},
year = {2017}
}