6 papers
On the Relationships between Domination, Isolation, and Packing
Geoffrey Boyer, Wayne Goddard, Michael A. Henning
We consider the relationships between the domination number of graph, denoted , and the distance- domination number, denoted , and three parameters that lie between th…
Small -kernels in digraphs with minimum in-degree
Geoffrey Boyer, Matt Burnham, Daniela Äerná +5
For a digraph , a subset is called a -kernel if is an independent set and all vertices in are reachable from via a directed path of length at…
All--Isolation in Trees
Geoffrey Boyer, Garrett C. Farrell, Wayne Goddard
We define an all--isolating set of a graph to be a set of vertices such that, if one removes and all its neighbors, then no component in what remains has order or mo…
Well-hued graphs with first difference two
Geoffrey Boyer, Kirsti Kuenzel, Jeremy Lyle +1
A graph is said to be well-hued if every maximal -colorable subgraph of has the same order . Therefore, if is well-hued, we can associate with a sequence $\…
On the Toughness of Regular Graphs and Prisms
Geoffrey Boyer, Wayne Goddard
We contribute results on -regular graphs that do and don't have the maximum possible toughness, namely . Doty and Ferland showed the existence of a -regular graph with t…
Bounds on Independent Isolation in Graphs
Geoffrey Boyer, Wayne Goddard
An isolating set of a graph is a set of vertices such that, if and its neighborhood is removed, only isolated vertices remain; and the isolation number is the minimum size…