Extremal Matching Energy of Complements of Trees

摘要

Gutman and Wagner proposed the concept of the matching energy which is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph. And they pointed out that the chemical applications of matching energy go back to the 1970s. Let T be a tree with n vertices. In this paper, we characterize the trees whose complements have the maximal, second-maximal and minimal matching energy. Furthermore, we determine the trees with edge-independence number p whose complements have the minimum matching energy for p = 1, 2, . . , [n/2]. When we restrict our consideration to all trees with a perfect matching, we determine the trees whose complements have the second-maximal matching energy.