On the construction of cospectral graphs for the adjacency and the normalized Laplacian matrices

2020/09/20 by M. Rajesh Kannan, Shivaramakrishna Pragada
Mathematics · Computer Science · #Graph theory and applications #Matrix Theory and Algorithms #Finite Group Theory Research

paper · doi:10.1080/03081087.2020.1821594

Abstract

In [A note about cospectral graphs for the adjacency and normalized Laplacian matrices. Linear Multilinear Algebra. 2010;58(3-4):387–390], Butler constructed a family of bipartite graphs, which are cospectral for both the adjacency and the normalized Laplacian matrices. In this article, we extend this construction for generating larger classes of bipartite graphs, which are cospectral for both the adjacency and the normalized Laplacian matrices. Also, we provide a couple of constructions of non-bipartite graphs, which are cospectral for the adjacency matrices but not necessarily for the normalized Laplacian matrices.

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