On minimal matching energy of unicyclic graphs with prescribed girth and pendent vertices - Li, Hong-Hai; Shi, Ming (Utilitas Mathematica, 2022)
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 Rn 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 Rl,1 n-k It is proved that among all unicyclic graphs except Ql,k n on n vertices with girth I and k pendent vertices, Rn l,k has the minimal matching energy. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.