On the Lexicographical Ordering by Spectral Moments of Bicyclic Graphs

Abstract

A graph \(G\) of order \(n\) is called a bicyclic graph if \(G\) is connected and the number of edges of \(G\) is \(n+ 1\). In this paper, we study the lexicographic ordering of bicyclic graphs by spectral moments. For each of the three basic types of bicyclic graphs on a fixed number of vertices maximal and minimal graphs in the mentioned order are determined.