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The graphs cospectral with the pineapple graph

Topcu,Hatice
; 
Sorgun,Sezer
; 
Haemers,W. H.
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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Date
2019-09
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Tilburg University Research Output Collection
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Keywords
adjacency matrix, cospectral graphs, spectral characterization, pineapple graph
Citation
Topcu, H, Sorgun, S & Haemers, W H 2019, 'The graphs cospectral with the pineapple graph', Discrete Applied Mathematics, vol. 269, pp. 52-59. https://doi.org/10.1016/j.dam.2018.10.002
URI
https://hdl.handle.net/20.500.14602/69763
License
info:eu-repo/semantics/closedAccess
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