Ordering of Unicyclic Graphs with Perfect Matchings by Minimal Matching Energies

Abstract

In 2012, Gutman and Wagner proposed the concept of the matching energy of a graph and pointed out that its chemical applications can go back to the 1970s. The matching energy of a graph is defined as the sum of the absolute values of the zeros of its matching polynomial. Let u and v be the non-isolated vertices of the graphs G and H with the same order, respectively.A fundamental problem encountered within the study of graph energy is the characterization of the graphs that belong to a given class of graphs having