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
Pages (from-to)52-59
JournalDiscrete Applied Mathematics
Volume269
Early online dateOct 2018
DOIs
Publication statusPublished - Sep 2019

Fingerprint

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

Topcu, Hatice ; Sorgun, Sezer ; Haemers, W. H. / The graphs cospectral with the pineapple graph. In: Discrete Applied Mathematics. 2019 ; Vol. 269. pp. 52-59.
@article{8519f1c072114a698eaa595a1e4f2df3,
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.",
keywords = "adjacency matrix, cospectral graphs, spectral characterization, pineapple graph",
author = "Hatice Topcu and Sezer Sorgun and Haemers, {W. H.}",
year = "2019",
month = "9",
doi = "10.1016/j.dam.2018.10.002",
language = "English",
volume = "269",
pages = "52--59",
journal = "Discrete Applied Mathematics",
issn = "0166-218X",
publisher = "Elsevier",

}

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

TY - JOUR

T1 - The graphs cospectral with the pineapple graph

AU - Topcu, Hatice

AU - Sorgun, Sezer

AU - Haemers, W. H.

PY - 2019/9

Y1 - 2019/9

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

VL - 269

SP - 52

EP - 59

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -