On minimal matching energy of unicyclic graphs with prescribed girth and pendent vertices

Abstract

Matching energy of a graph is introduced by Gutman and Wagner recently, and can be defined as the sum of the absolute values of zeros of its matching polynomial. Let R_n ^l,k denote the unicyclic graph of order n obtained from a cycle Cl by attaching k-1 pendent edges and one pendent path at a vertex in the cycle. Denote by Ql,kn the unicyclic graph obtained from attaching k pendent edges at the (unique) pendent vertex of R^l,1 _n-k It is proved that among all unicyclic graphs except Q^l,k _n on n vertices with girth I and k pendent vertices, R_n ^l,k has the minimal matching energy. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.