Aα-Spectral Characterizations of Some Joins

Abstract EN

Let G be a graph with n vertices.

For every real α∈0,1, write AαG for the matrix AαG=αDG+1−αAG, where AG and DG denote the adjacency matrix and the degree matrix of G, respectively.

The collection of eigenvalues of AαG together with multiplicities are called the Aα-spectrum of G.

A graph G is said to be determined by its Aα-spectrum if all graphs having the same Aα-spectrum as G are isomorphic to G.

In this paper, we show that some joins are determined by their Aα-spectra for α∈0,1/2 or 1/2,1.