Extremal Values of Variable Sum Exdeg Index for Conjugated Bicyclic Graphs

Abstract

A connected graph $G\left(V,E\right)$ in which the number of edges is one more than its number of vertices is called a bicyclic graph. A perfect matching of a graph is a matching in which every vertex of the graph is incident to exactly one edge of the matching set such that the number of vertices is two times its matching number. In this paper, we investigated maximum and minimum values of variable sum exdeg index, ${\text{SEI}}_a$ for bicyclic graphs with perfect matching for $k\ge 5$ and $a>1$ .