Characteristic polynomial of a generalized complete product of matrices |
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Authors: | Suk-Geun Hwang Jin-Woo Park |
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Institution: | Department of Mathematics Education, Kyungpook National University, Taegu 702-701, Republic of Korea |
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Abstract: | For a simple graph G, let denote the complement of G relative to the complete graph and let PG(x)=det(xI-A(G)) where A(G) denotes the adjacency matrix of G. The complete product G∇H of two simple graphs G and H is the graph obtained from G and H by joining every vertex of G to every vertex of H. In 2]PG∇H(x) is represented in terms of PG, , PH 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. |
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Keywords: | 15A15 05C50 05C76 |
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