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 Operations Research

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

1 Citation (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 - Sep 2019

Keywords

adjacency matrix
cospectral graphs
spectral characterization
pineapple graph

Access to Document

10.1016/j.dam.2018.10.002

Fingerprint Dive into the research topics of 'The graphs cospectral with the pineapple graph'. Together they form a unique fingerprint.

Cite this

@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 = sep,

doi = "10.1016/j.dam.2018.10.002",

language = "English",

volume = "269",

pages = "52--59",

journal = "Discrete Applied Mathematics",

issn = "0166-218X",

publisher = "Elsevier",

}

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 -