The Spectral Characterization of Graphs of Index Less Than $2$ with no $Z_n$ as a Component

Abstract

A graph is said to be determined by its adjacency spectrum (or to be a DS graph, for short) if there is no other non-isomorphic graph with the same adjacency spectrum. Although all connected graphs of index less than $2$ are known to be determined by their adjacency spectra, the classification of DS graphs of index less than $2$ is not complete yet. The purpose of this paper is to characterize all DS graphs of index less than $2$ with no $Z_n$ as a component.