The graphs cospectral with the pineapple graph

Hatice Topcu, Sezer Sorgun, W. H. Haemers

Research output: Contribution to journalArticleScientificpeer-review

Abstract

The pineapple graph is obtained by appending q pendant edges to a vertex of a complete graph. We prove that among connected graphs, the pineapple graph is determined by its adjacency spectrum. Moreover, we determine all disconnected graphs which are cospectral with a pineapple graph. Thus we find for which values of p and q the pineapple graph is determined by its adjacency spectrum. The main tool is a recent classification of all graphs with all but three eigenvalues equal to 0 or -1 by the third author.
Original languageEnglish
JournalDiscrete Applied Mathematics
DOIs
Publication statusE-pub ahead of print - Oct 2018

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Cospectral Graphs
Graph in graph theory
Adjacency
Complete Graph
Connected graph
Eigenvalue
Vertex of a graph

Keywords

  • adjacency matrix
  • cospectral graphs
  • spectral characterization
  • pineapple graph

Cite this

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author = "Hatice Topcu and Sezer Sorgun and Haemers, {W. H.}",
year = "2018",
month = "10",
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language = "English",
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The graphs cospectral with the pineapple graph. / Topcu, Hatice; Sorgun, Sezer; Haemers, W. H.

In: Discrete Applied Mathematics, 10.2018.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Haemers, W. H.

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N2 - The pineapple graph is obtained by appending q pendant edges to a vertex of a complete graph. We prove that among connected graphs, the pineapple graph is determined by its adjacency spectrum. Moreover, we determine all disconnected graphs which are cospectral with a pineapple graph. Thus we find for which values of p and q the pineapple graph is determined by its adjacency spectrum. The main tool is a recent classification of all graphs with all but three eigenvalues equal to 0 or -1 by the third author.

AB - The pineapple graph is obtained by appending q pendant edges to a vertex of a complete graph. We prove that among connected graphs, the pineapple graph is determined by its adjacency spectrum. Moreover, we determine all disconnected graphs which are cospectral with a pineapple graph. Thus we find for which values of p and q the pineapple graph is determined by its adjacency spectrum. The main tool is a recent classification of all graphs with all but three eigenvalues equal to 0 or -1 by the third author.

KW - adjacency matrix

KW - cospectral graphs

KW - spectral characterization

KW - pineapple graph

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DO - 10.1016/j.dam.2018.10.002

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JF - Discrete Applied Mathematics

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