Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Gary Chartrand

Second Advisor

Dr. Joseph A. Gallian

Third Advisor

Dr. Clifton Ealy

Fourth Advisor

Dr. Kenneth Williams


The defining properties of several important subgraphs and subdigraphs rely on the concept of distance in graphs and digraphs. In this dissertation, we investigate many of these subgraphs and subdigraphs.

In Chapter I, we present some preliminary definitions and examples. In addition, many known results are recalled. We then introduce several new induced subgraphs and subdigraphs.

In Chapter n, we investigate the general structure of the center and periphery of a graph. We introduce two new induced subgraphs of the center along with a new induced subgraph of the periphery of a graph in order to study these structures.

For every digraph D , there is a corresponding digraph whose vertex set consists of subsets of vertices of D of the same cardinality. In Chapter III, we introduce this multivertex digraph and indicate the motivation for studying these digraphs.

The center and periphery are subgraphs or subdigraphs induced by those vertices of minimum and maximum eccentricity, respectively. In Chapter IV, we introduce two new induced subgraphs and subdigraphs that involve the remaining vertices and investigate their relative location in the graph or digraph.

We continue this investigation in Chapter V by studying the relative location of the median and periphery of a graph or digraph.

Access Setting

Dissertation-Open Access