Aα-Spectral Characterizations of Some Joins
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 t...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/8294312 |
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| author | Tingzeng Wu Tian Zhou |
| author_facet | Tingzeng Wu Tian Zhou |
| author_sort | Tingzeng Wu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a133a806b6c7483c9d95d0d838105d7f |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-a133a806b6c7483c9d95d0d838105d7f2025-02-03T06:45:52ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/82943128294312Aα-Spectral Characterizations of Some JoinsTingzeng Wu0Tian Zhou1School of Mathematics and Statistics, Qinghai Nationalities University, Xining, Qinghai 810007, ChinaSchool of Mathematics and Statistics, Qinghai Nationalities University, Xining, Qinghai 810007, ChinaLet 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.http://dx.doi.org/10.1155/2020/8294312 |
| spellingShingle | Tingzeng Wu Tian Zhou Aα-Spectral Characterizations of Some Joins Journal of Mathematics |
| title | Aα-Spectral Characterizations of Some Joins |
| title_full | Aα-Spectral Characterizations of Some Joins |
| title_fullStr | Aα-Spectral Characterizations of Some Joins |
| title_full_unstemmed | Aα-Spectral Characterizations of Some Joins |
| title_short | Aα-Spectral Characterizations of Some Joins |
| title_sort | aα spectral characterizations of some joins |
| url | http://dx.doi.org/10.1155/2020/8294312 |
| work_keys_str_mv | AT tingzengwu aaspectralcharacterizationsofsomejoins AT tianzhou aaspectralcharacterizationsofsomejoins |