Abstract
Let G=( V, E) be a undirected graph containing n vertices, and let M G be the set of all Hermitian n× n matrices M=( m i, j ) with m i, j ≠0 if i and j are connected by one edge of G, with m i,j∈ C if i and j are connected by at least two edges, with m i, j =0 if i≠ j, and i and j are not connected by an edge of G, and with m i, i for i=1,…, n a real number. What is the largest nullity attained by any positive semi-definite matrix M∈ M G ? In this paper we characterize, for t=1 and 2, those graphs G for which the maximum nullity is not greater than t.
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