  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.
