2019/02/02 by M. Souri, Souri, M., F. Heydari +3
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1902.00747
openalex publication_date 2019/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a simple graph and A(G) be the adjacency matrix of G. The matrix S(G) = J -I -2A(G) is called the Seidel matrix of G, where I is an identity matrix and J is a square matrix all of whose entries are equal to 1. Clearly, if G is a graph of order n with no isolated vertex, then the Seidel matrix of G is also the adjacency matrix of a signed complete graph Kn whose negative edges induce G. In this paper, we study the Seidel eigenvalues of the complete multipartite graph Kn1,…,nk and investigate its Seidel characteristic polynomial. We show that if there are at least three parts of size ni, for some i=1,…,k, then Kn1,…,nk is determined, up to switching, by its Seidel spectrum.