Zero forcing is an iterative coloring procedure on a graph that starts by initially coloring vertices white and blue and then repeatedly applies the following rule: if any blue vertex has a uniqueâ€¦ (More)

The distance matrix D(G) = [dij ] of a graph G is the matrix indexed by the vertices {v1, . . . , vn} of G where dij = d(vi, vj) is the distance between the vertices vi and vj , i.e., the length of aâ€¦ (More)

For a given graph G and an associated class of real symmetric matrices whose offdiagonal entries are governed by the adjacencies in G, the collection of all possible spectra for such matrices isâ€¦ (More)

A traditional Nordhaus-Gaddum problem for a graph parameter Î² is to find a (tight) upper or lower bound on the sum or product of Î²(G) and Î²(G) (where G denotes the complement of G). Anâ€¦ (More)

Zero forcing is an iterative process on a graph used to bound the maximum nullity. The process begins with select vertices as colored, and the remaining vertices can become colored under a specificâ€¦ (More)

Tanglegrams are special graphs that consist of a pair of rooted binary trees with the same number of leaves, and a perfect matching between the two leaf-sets. These objects are of use inâ€¦ (More)