A k-ranking of a graph G is a labeling of the vertices of G with values from {1, . . . , k} such that any path joining two vertices with the same label contains a vertex having a higher label. Theâ€¦ (More)

We consider the problem of computing inertia sets for graphs. By using tools for combining the inertia sets of smaller graphs we can reduce this problem to understanding the inertia sets forâ€¦ (More)

Abstract. Let G be an undirected graph on n vertices and let S(G) be the set of all real symmetric nÃ—n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to theâ€¦ (More)

A sign pattern matrix is a matrix whose entries are from the set {+,âˆ’, 0}. The minimum rank of a sign pattern matrix A is the minimum of the ranks of the real matrices whose entries have signs equalâ€¦ (More)

Let F be a field, let G be a simple graph on n vertices, and let S (G) be the class of all F -valued symmetric n Ã— n matrices whose nonzero off-diagonal entries occur in exactly the positionsâ€¦ (More)

The principal permanent rank characteristic sequence is a binary sequence r0r1 Â· Â· Â· rn where rk = 1 if there exists a principal square submatrix of size k with nonzero permanent and rk = 0â€¦ (More)

Let G be a simple undirected graph on n vertices and let S(G) be the class of real symmetric nÃ— n matrices whose nonzero off-diagonal entries correspond exactly to the edges of G. Given 2n âˆ’ 1 realâ€¦ (More)

Let F be a field, let G be a simple graph on n vertices, and let S (G) be the class of all F -valued symmetric n Ã— n matrices whose nonzero off-diagonal entries occur in exactly the positionsâ€¦ (More)