فهرست نشریات علمی دسترسی آزاد ایران

The matching polynomial of a graph has coefficients that give the number of matchings in the graph. In this paper, we determine all connected graphs with maximum vertex degree four whose matching polynomials have only integer zeros. A graph is matching integral if the zeros of its matching polynomial are all integers. We show that there are exactly two matching integral graphs with maximum vertex degree four.