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.