Characteristic polynomial of a generalized complete product of matrices

Abstract: For a simple graph , let denote the complement of relative to the complete graph and let where denotes the adjacency matrix of . The complete product of two simple graphs and is the graph obtained from and by joining every vertex of to every vertex of . In is represented in terms of , , and . In this paper we extend the notion of complete product of simple graphs to that of generalized complete product of matrices and obtain their characteristic polynomials. [ABSTRACT FROM AUTHOR]