Abstract. The zero forcing number Z(G), which is the minimum number of vertices in a zero forcing set of a 1 graph G, is used to study the maximum nullity/minimum rank of the family of symmetricâ€¦ (More)

The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i 6= j) is nonzero whenever {i, j} is an edge in G and is zeroâ€¦ (More)

Let G = (V, E) be a multigraph with no loops on the vertex set V = {1, 2, . . . , n}. Define S+(G) as the set of symmetric positive semidefinite matrices A = [aij ] with aij 6= 0, i 6= j, if ij âˆˆâ€¦ (More)

For a given undirected graph G, the minimum rank of G is defined to be the smallest possible rank over all real symmetric matrices A whose (i, j)th entry is nonzero whenever i 6= j and {i, j} is anâ€¦ (More)

The minimum rank of a graph has been an interesting and well studied parameter 6 investigated by many researchers over the past decade or so. One of the many unresolved questions on 7 this topic isâ€¦ (More)

For a given acyclic graph G, an important problem is to characterize all of the eigenvalues over all symmetric matrices with graph G. Of particular interest is the connection between this standardâ€¦ (More)

The main problem of interest is to investigate how the algebraic connectivity o f a weighted connected graph behaves when the graph is perturbed by removing one or more connected components at a xedâ€¦ (More)

Tree-width, and variants that restrict the allowable tree decompositions, play an important role in the study of graph algorithms and have application to computer science. The zero forcing number isâ€¦ (More)