Superuser Pansophy

Abstract

Given a graph $G$, we are interested in finding disjoint paths for a given set of distinct pairs of vertices. In 2017, we formally defined a new parameter, the pansophy of $G$, in the context of the disjoint path problem.

In this paper, we investigate the pansophy of two classes of graphs that contain a vertex that we define as the superuser. The superuser of a graph is a vertex that is adjacent to every other vertex. We close with future research directions.