# 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 language English 52-59 Discrete Applied Mathematics 269 Oct 2018 https://doi.org/10.1016/j.dam.2018.10.002 Published - Sep 2019

### Fingerprint

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

### Keywords

• cospectral graphs
• spectral characterization
• pineapple graph

### Cite this

Topcu, Hatice ; Sorgun, Sezer ; Haemers, W. H. / The graphs cospectral with the pineapple graph. In: Discrete Applied Mathematics. 2019 ; Vol. 269. pp. 52-59.
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The graphs cospectral with the pineapple graph. / Topcu, Hatice; Sorgun, Sezer; Haemers, W. H.

In: Discrete Applied Mathematics, Vol. 269, 09.2019, p. 52-59.

Research output: Contribution to journalArticleScientificpeer-review

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T1 - The graphs cospectral with the pineapple graph

AU - Topcu, Hatice

AU - Sorgun, Sezer

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 - cospectral graphs

KW - spectral characterization

KW - pineapple graph

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DO - 10.1016/j.dam.2018.10.002

M3 - Article

VL - 269

SP - 52

EP - 59

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

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