Degree
Doctor of Philosophy
Program
Computer Science
Supervisor
Dr. Roberto Solis-Oba
Abstract
The L(2,1) -labeling problem has been extensively researched on many graph classes. In this thesis, we have also studied the problem on some particular classes of graphs.
In Chapter 2 we present a new general approach to derive upper bounds for L(2,1)-labeling numbers and applied that approach to derive bounds for the four standard graph products.
In Chapter 3 we study the L(2,1)-labeling number of the composition of n graphs.
In Chapter 4 we consider the Cartesian sum of graphs and derive, both, lower and upper bounds for their L(2,1)-labeling number. We use two different approaches to derive the upper bounds and both approaches improve previously known bounds. We also present new approximation algorithms for the L(2,1 )-labeling problem on Cartesian sum graphs.
In Chapter 5, we characterize d-disk graphs for d>1, and give the first upper bounds on the L(2,1)-labeling number for this class of graphs.
In Chapter 6, we compute upper bounds for the L(2,1)-labeling number of total graphs of K_{1,n}-free graphs.
In Chapter 7, we study the four standard products of graphs using the adjacency matrix analysis approach.
In Chapter 8, we determine the exact value for the L(2,1)-labeling number of a particular class of Mycielski graphs. We also provide, both, lower and upper bounds for the L(2,1)-labeling number of any Mycielski graph.
Recommended Citation
Shao, Zhendong, "The Research on the L(2,1)-labeling problem from Graph theoretic and Graph Algorithmic Approaches" (2012). Electronic Thesis and Dissertation Repository. 494.
https://ir.lib.uwo.ca/etd/494