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The graphs cospectral with the pineapple graph

Topcu, Hatice; Sorgun, Sezer; Haemers, Willem H.


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        "affiliation": "Nevsehir Haci Bektas Veli Univ, Dept Math, Nevsehir, Turkey", 
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    "description": "The pineapple graph K-p(q) is obtained by appending q pendant edges to a vertex of a complete graph K-p (p >= 3, q >= 1). 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 K-p(q) 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. (C) 2018 Elsevier B.V. All rights reserved.", 
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Topcu, H., Sorgun, S. ve Haemers, W. H. (2019). The graphs cospectral with the pineapple graph. DISCRETE APPLIED MATHEMATICS, 269, 52–59. doi:10.1016/j.dam.2018.10.002

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