On the spectral characterization of mixed extensions of P-3

Willem H. Haemers*, Sezer Sorgun, Hatice Topcu

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

A mixed extension of a graph G is a graph H obtained from G by replacing each vertex of G by a clique or a coclique, whilst two vertices in H corresponding to distinct vertices x and y of G are adjacent whenever x and y are adjacent in G. If G is the path P-3, then H has at most three adjacency eigenvalues unequal to 0 and -1. Recently, the first author classified the graphs with the mentioned eigenvalue property. Using this classification we investigate mixed extension of P-3 on being determined by the adjacency spectrum. We present several cospectral families, and with the help of a computer we find all graphs on at most 25 vertices that are cospectral with a mixed extension of P-3.
Original languageEnglish
Article numberP3.16
Number of pages10
JournalThe Electronic Journal of Combinatorics: EJC
Volume26
Issue number3
Publication statusPublished - 19 Jul 2019

Cite this

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title = "On the spectral characterization of mixed extensions of P-3",
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On the spectral characterization of mixed extensions of P-3. / Haemers, Willem H.; Sorgun, Sezer; Topcu, Hatice.

In: The Electronic Journal of Combinatorics: EJC, Vol. 26, No. 3, P3.16, 19.07.2019.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - On the spectral characterization of mixed extensions of P-3

AU - Haemers, Willem H.

AU - Sorgun, Sezer

AU - Topcu, Hatice

PY - 2019/7/19

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N2 - A mixed extension of a graph G is a graph H obtained from G by replacing each vertex of G by a clique or a coclique, whilst two vertices in H corresponding to distinct vertices x and y of G are adjacent whenever x and y are adjacent in G. If G is the path P-3, then H has at most three adjacency eigenvalues unequal to 0 and -1. Recently, the first author classified the graphs with the mentioned eigenvalue property. Using this classification we investigate mixed extension of P-3 on being determined by the adjacency spectrum. We present several cospectral families, and with the help of a computer we find all graphs on at most 25 vertices that are cospectral with a mixed extension of P-3.

AB - A mixed extension of a graph G is a graph H obtained from G by replacing each vertex of G by a clique or a coclique, whilst two vertices in H corresponding to distinct vertices x and y of G are adjacent whenever x and y are adjacent in G. If G is the path P-3, then H has at most three adjacency eigenvalues unequal to 0 and -1. Recently, the first author classified the graphs with the mentioned eigenvalue property. Using this classification we investigate mixed extension of P-3 on being determined by the adjacency spectrum. We present several cospectral families, and with the help of a computer we find all graphs on at most 25 vertices that are cospectral with a mixed extension of P-3.

M3 - Article

VL - 26

JO - The Electronic Journal of Combinatorics: EJC

JF - The Electronic Journal of Combinatorics: EJC

SN - 1097-1440

IS - 3

M1 - P3.16

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