The graphs which are cospectral with the generalized pineapple graph

2023/07/24 by Li, Borchen, Ji, Qingzhong
#05C05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.12501

Abstract

Let p, k, q be positive integers with p-2 \geqslant k and let K_p,k^q be the generalized pineapple graph which is obtained by joining independent set of q vertices with k vertices of a complete graph K_p. In \citeTSH2, Haemers et al. constructed graphs which cospectral with K_p,1^q. In this paper, we determine all graphs which are cospectral with K_p,k^q by considering the eigenvalues of its adjacency matrix. Moreover, We extend the conclusions of Haemers et al. to a broader context.

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