Date of Award

4-2022

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Ping Zhang, Ph.D.

Second Advisor

Gary Chartrand, Ph.D.

Third Advisor

Jeffery Strom, Ph.D.

Fourth Advisor

Ben Salisbury, Ph.D.

Keywords

Domination, irregular, orbital

Abstract

In recent decades, domination in graphs has become a popular area of study due in large degree to its applications to modern society and the mathematical beauty of the topic. While this area evidently began with the work of Claude Berge in 1958 and of Oystein Ore in 1962, domination did not become an active area of research until 1977 with the appearance of a survey paper by Ernest Cockayne and Stephen Hedetniemi. Since then a large number of variations of domination have surfaced and provided numerous applications to different areas of science and real-life problems. Among these variations are domination parameters defined in terms of distance and vertex orbits which provide a more general setting for domination in graphs. In this research, we study a new graph domination concept referred to as irregular orbital domination in graphs. This concept describes domination in the view of distance, vertex orbits, and graph labelings together with the well-known topic of irregularity in graphs. We determine the existence of irregular orbital domination for several well-studied classes of graphs, investigate structural and extremal problems dealing with irregular orbital domination in graphs, and explore relationships among this domination concept and traditional domination concepts.

Access Setting

Dissertation-Open Access

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Included in

Mathematics Commons

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