The graphs cospectral with the pineapple graph

Hatice Topcu; Sezer Sorgun; W. H. Haemers

doi:10.1016/j.dam.2018.10.002

The graphs cospectral with the pineapple graph

Hatice Topcu, Sezer Sorgun, W. H. Haemers

Econometrics and OR

Research output: Contribution to journal › Article › Scientific › peer-review

9 Citations (Scopus)

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
Pages (from-to)	52-59
Journal	Discrete Applied Mathematics
Volume	269
Early online date	Oct 2018
DOIs	https://doi.org/10.1016/j.dam.2018.10.002
Publication status	Published - Sept 2019

Keywords

adjacency matrix
cospectral graphs
spectral characterization
pineapple graph

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10.1016/j.dam.2018.10.002

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title = "The graphs cospectral with the pineapple graph",

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.",

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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 - adjacency matrix

KW - cospectral graphs

KW - spectral characterization

KW - pineapple graph

U2 - 10.1016/j.dam.2018.10.002

DO - 10.1016/j.dam.2018.10.002

M3 - Article

SN - 0166-218X

VL - 269

SP - 52

EP - 59

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

The graphs cospectral with the pineapple graph

Abstract

Keywords

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