Graphs with integer matching polynomial zeros

In this paper, we study graphs whose matching polynomials 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 K-7 \ (E(C-3) boolean OR E(C-4)) 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. (C) 2017 Elsevier B.V. All rights reserved