Jason Hedetniemi

  • Citations Per Year
Learn More
For any given type of a set of vertices in a connected graph G = (V,E), we seek to determine the smallest integers (x, y : z) such that all minimal (or maximal) sets S of the given type, where |V | > |S| ≥ 2, have the property that every vertex v ∈ V − S is within distance at most x to a vertex u ∈ S (shortest distance), and within distance at most y to a(More)
Unique minimum dominating sets in the Cartesian product of a graph and a Hamming graph are considered. A characterization of such sets is given, when they exist. A necessary and sufficient condition for the existence of a unique minimum dominating set is given in the special case of the Cartesian product of a tree and multiple copies of the same complete(More)
In this paper, we consider graphs having a unique minimum independent dominating set. We first discuss the effects of deleting a vertex, or the closed neighborhood of a vertex, from such graphs. We then discuss five operations which, in certain circumstances, can be used to combine two graphs, each having a unique minimum independent dominating set, to(More)
  • 1