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Aα-Spectral Characterizations of Some Joins

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  • Tingzeng Wu
  • Tian Zhou
  • Naihuan Jing

Abstract

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.

Suggested Citation

  • Tingzeng Wu & Tian Zhou & Naihuan Jing, 2020. "Aα-Spectral Characterizations of Some Joins," Journal of Mathematics, Hindawi, vol. 2020, pages 1-8, December.
    • Handle: RePEc:hin:jjmath:8294312
    DOI: 10.1155/2020/8294312
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