Spectral Determination of a Class of Tricyclic Graphs

Abstract

A \(T\)-shape tree is a tree with exactly one of its vertices having maximal degree \(3\). In this paper, we consider a class of tricyclic graphs which is obtained from a \(T\)-shape tree by attaching three identical odd cycles \(C_ks\) to three vertices of degree \(1\) of the \(T\)-shape tree, respectively, where \(k \geq 3\) is odd. It is shown that such graphs are determined by their adjacency spectrum.