Date of Award
4-2020
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
Dr.Ping Zhang
Second Advisor
Dr. Patrick Bennett
Third Advisor
Dr. Gary Chartrand
Fourth Advisor
Dr. Dinesh Sarvate
Keywords
Royal coloring, mean coloring, graph theory, graph coloring, extremal graphs, color-induced
Abstract
Graph coloring is one of the most popular areas of graph theory, no doubt due to its many fascinating problems and applications to modern society, as well as the sheer mathematical beauty of the subject. As far back as 1880, in an attempt to solve the famous Four Color Problem, there have been numerous examples of certain types of graph colorings that have generated other graph colorings of interest. These types of colorings only gained momentum a century later, however, when in the 1980s, edge colorings were studied that led to vertex colorings of various types, led by the introduction of the irregularity strength of a graph by Chartrand and the majestic chromatic index of a graph by Harary and Plantholt. Since then, the study of such graph colorings has become a popular area of research in graph theory. Recently, two set and number theoretic graph colorings were introduced, namely royal colorings and rainbow mean colorings. These two colorings as well as variations have extended some classical graph coloring concepts. We investigate structural and extremal problems dealing with royal and rainbow mean colorings and explore relationships among the chromatic parameters resulting from these colorings and traditional chromatic parameters.
Access Setting
Dissertation-Open Access
Recommended Citation
Hallas, James, "Extremal Problems on Induced Graph Colorings" (2020). Dissertations. 3611.
https://scholarworks.wmich.edu/dissertations/3611