On the Laplacian Spectral Radii of Tricyclic Graphs

Abstract

A graph \(G\) of order \(n\) is called a tricyclic graph if \(G\) is connected and the number of edges of \(G\) is \(n + 2\). Let \(\mathcal{T}_n\) denote the set of all tricyclic graphs on \(n\) vertices. In this paper, we determine the first to nineteenth largest Laplacian spectral radii among all graphs in the class \(\mathcal{T}_n\) (for \(n \geq 11\)), together with the corresponding graphs.