Matching Energy of Graphs with Maximum Degree at Most 3

Abstract

The matching energy of a graph G, denoted by ME(G), is def ined as the sum of absolute values of the zeros of the matching polynomial of G. In this paper, we prove that if G is a connected graph of order n with maximum degree at most 3, then ME(G) > n with only six exceptions. In particular, we show that there are only two connected graphs with maximum degree at most three, whose matching energies are equal to the number of vertices.