7 papers · 1 filter
Constructing solvable groups whose character degree graphs generalize the bowtie
Jacob Laubacher, Mark L. Lewis, Lorenzo Ravaglia +1
We present here a generalized construction of a finite solvable group whose prime character degree graph has the shape and structure of the bowtie graph. As with the original bowti…
On prime character degree graphs occurring within a family of graphs (iii)
Mark W. Bissler, Thatcher Debowski, Theodore F. Hoelker +3
We conclude the classification work done in the two previous papers of the same name. Here we add flexibility to the construction, thereby viewing the graphs in full generality. Ou…
On the metric dimension of the character degree graph of a solvable group
Peter J. Cameron, G. Sivanesan, C. Selvaraj +2
Let be a finite solvable group and let be the character degree graph of . In this paper, we obtain the metric dimension of certain character degree graphs. Specifical…
Classifying character degree graphs with seven vertices
Jacob Laubacher, Mark Medwid, Dylan Schuster
We study here the graphs with seven vertices in an effort to classify which of them appear as the prime character degree graphs of finite solvable groups. This classification is co…
On prime character degree graphs occurring within a family of graphs (ii)
Sara DeGroot, Jacob Laubacher, Mark Medwid
In this paper, we continue the classification work done in the first paper of the same name. With careful modifications of our previous approach, we are able to deduce (with two no…
On prime character degree graphs occurring within a family of graphs
Jacob Laubacher, Mark Medwid
In this paper we investigate families of connected graphs which do not contain an odd cycle in their complement. Specifically, we consider graphs formed by two complete graphs conn…