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

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

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Keywords

adjacency matrix
cospectral graphs
spectral characterization
pineapple graph

Cite this

Topcu, H., Sorgun, S., & Haemers, W. H. (2019). The graphs cospectral with the pineapple graph. Discrete Applied Mathematics, 269, 52-59. https://doi.org/10.1016/j.dam.2018.10.002

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Access to Document

10.1016/j.dam.2018.10.002