Abstract
It is known that complete multipartite graphs are determined by their distance spectrum but not by their adjacency spectrum. The Seidel spectrum of a graph G on more than one vertex does not determine the graph, since any graph obtained from G by Seidel switching has the same Seidel spectrum. We consider G to be determined by its Seidel spectrum, up to switching, if any graph with the same spectrum is switching equivalent to a graph isomorphic to G. It is shown that any graph which has the same spectrum as a complete k-partite graph is switching equivalent to a complete k-partite graph, and if the different partition sets sizes are p1,…,pl, and there are at least three partition sets of each size pi, i=1,…,l, then G is determined, up to switching, by its Seidel spectrum. Sufficient conditions for a complete tripartite graph to be determined by its Seidel spectrum are discussed.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
