Inertia and biclique decompositions of joins of graphs

Authors:
David A. Gregory;Brenda Heyink;Kevin N. Vander Meulen
Affiliations:
Department of Mathematics and Statistics, Queen's University, Jeffrey Hall, Kingston, Ont. Canada K7L 3N6;Department of Mathematics, Redeemer University College, Ancaster, Ont. Canada L9K 1J4;Department of Mathematics, Redeemer University College, Ancaster, Ont. Canada L9K 1J4
Venue:
Journal of Combinatorial Theory Series B
Year:
2003

Citing 3
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Abstract

We characterize the inertia of A + B for Hermitian matrices A and B when the rank of B is one. We use this to characterize the inertia of a partial join of two graphs. We then provide graph joins G for which the minimum number of complete bipartite graphs needed in a partition of the edge multi-set of G is equal to the maximum of the number of positive and negative Eigenvalues of G.