Inertia and biclique decompositions of joins of graphs (Q1405108)

The authors characterize the inertia of \(A+B\) for Hermitian matrices \(A\) and \(B\) when the rank of \(B\) is one. Using this, the inertia of a partial join of two graphs has been characterized. The authors further provide graph joins \(G\) for which the minimum number of complete bipartite graphs needed in a partition of the edge multiset of \(G\) is equal to the maximum of the number of positive and negative eigenvalues of \(G\).