4 citations · 10 across the 6 of their papers we have counts for
7 papers
Independent Domination in Directed Graphs
Michael Cary, Jonathan Cary, Savari Prabhu
In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent d…
A Linear Algorithm for Minimum Dominator Colorings of Orientations of Paths
Michael Cary
In this paper we present an algorithm for finding a minimum dominator coloring of orientations of paths. To date this is the first algorithm for dominator colorings of digraphs in…
Dominator Chromatic Numbers of Orientations of Trees
Michael Cary
In this paper we prove that the dominator chromatic number of every oriented tree is invariant under reversal of orientation. In addition to this marquee result, we also prove the…
Dominator Colorings of Digraphs
Michael Cary
This paper serves as the first extension of the topic of dominator colorings of graphs to the setting of digraphs. We establish the dominator chromatic number over all possible ori…
Cycle Intersection Graphs and Minimum Decycling Sets of Even Graphs
Michael Cary
We introduce the cycle intersection graph of a graph, an adaptation of the cycle graph of a graph, and use the structure of these graphs to prove an upper bound for the decycling n…
Vertices with the Second Neighborhood Property in Eulerian Digraphs
Michael Cary
The Second Neighborhood Conjecture states that every simple digraph has a vertex whose second out-neighborhood is at least as large as its first out-neighborhood, i.e. a vertex wit…
One-sided Duo rings are McCoy
Michael Cary
In this paper we prove that one-sided Duo rings are (two-sided) McCoy. By doing so, we are then able to explicitly describe some of these ring element annihilators of polynomials i…