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 $C_{k}s$ to three vertices of degree $1$ of the $T$-shape tree, respectively, where $k\ge 3$ is odd. It is shown that such graphs are determined by their adjacency spectrum.