Constructing cospectral graphs by unfolding non-bipartite graphs
arXiv:2401.03035 · doi:10.1016/j.dam.2024.06.016
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.
arXiv admin note: text overlap with arXiv:2110.09034