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arXiv · 2401.03035

Constructing cospectral graphs by unfolding non-bipartite graphs

M. Rajesh Kannan·Shivaramakrishna Pragada·Hitesh Wankhede
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Abstract

In 2010, Butler introduced the unfolding operation on a bipartite graph to produce two bipartite graphs, which are cospectral for the adjacency and the normalized Laplacian matrices. In this article, we describe how the idea of unfolding a bipartite graph with respect to another bipartite graph can be extended to nonbipartite graphs. In particular, we describe how unfoldings involving reflexive bipartite, semi-reflexive bipartite, and multipartite graphs are used to obtain cospectral nonisomorphic graphs for the adjacency matrix.

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M. Rajesh Kannan, Shivaramakrishna Pragada, Hitesh Wankhede. 2024-04-30. Constructing cospectral graphs by unfolding non-bipartite graphs. https://doi.org/10.1016/j.dam.2024.06.016

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