On the spectral characterization of mixed extensions of P3

Willem H. Haemers, Sezer Sorgun, Hatice Topcu

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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 P3, 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 P3 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 P3.
Original languageEnglish
Place of PublicationIthaca
PublisherCornell University Library
Number of pages10
Publication statusPublished - 30 Oct 2018

Publication series

NamearXiv
Volume1810.12615

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Adjacency
Graph in graph theory
Adjacent
Eigenvalue
Unequal
Clique
Distinct
Path
Vertex of a graph
Family

Cite this

Haemers, W. H., Sorgun, S., & Topcu, H. (2018). On the spectral characterization of mixed extensions of P3. (arXiv; Vol. 1810.12615). Ithaca: Cornell University Library.
Haemers, Willem H. ; Sorgun, Sezer ; Topcu, Hatice. / On the spectral characterization of mixed extensions of P3. Ithaca : Cornell University Library, 2018. (arXiv).
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Haemers, WH, Sorgun, S & Topcu, H 2018 'On the spectral characterization of mixed extensions of P3' arXiv, vol. 1810.12615, Cornell University Library, Ithaca.

On the spectral characterization of mixed extensions of P3. / Haemers, Willem H.; Sorgun, Sezer; Topcu, Hatice.

Ithaca : Cornell University Library, 2018. (arXiv; Vol. 1810.12615).

Research output: Working paperOther research output

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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 P3, 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 P3 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 P3.

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Haemers WH, Sorgun S, Topcu H. On the spectral characterization of mixed extensions of P3. Ithaca: Cornell University Library. 2018 Oct 30. (arXiv).