Date of Award

6-1991

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Dr. Gary Chartrand

Second Advisor

Dr. Shashi F. Kapoor

Third Advisor

Dr. Dalia Motzkin

Fourth Advisor

Dr. Maciej M. Syslo

Abstract

Some distances defined on graphs depend on transforming one graph into another. Two of these transformations are edge rotation and edge slide. In this dissertation, extensions and generalizations of these transformations are investigated.

Chapter I begins with some preliminary definitions and known results. Then two types of digraph transformations are introduced and their properties are studied.

Some measures of distance between graphs and distance between digraphs are defined in Chapter II. Also distance graphs and digraphs associated with these measures are introduced. Several known results concerning this topic are generalized and new results are presented.

Chapter III is devoted to F-transformations, which is a generalization of the previously discussed transformations of graphs. Based on F-transformations, a new measure of distance between graphs and a new class of distance graphs (called F-distance graphs) are introduced. A characterization of graphs that are F-distance graphs is investigated.

Transformations of subgraphs and related topics are studied in Chapter IV.

Comments

Fifth Advisor: Arthur T. White

Access Setting

Dissertation-Open Access

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