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

Keywords

  • adjacency matrix
  • cospectral graphs
  • spectral characterization
  • pineapple graph

Cite this