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• W50590809 abstract "Graph coloring is one of the most popular topics in graph theory and many advances in graph theory are a direct consequence of graph coloring research. The L(2, 1)-labeling problem is a generalization of the vertex coloring problem and its application background is the frequency assignment problem. 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 obtain upper bounds for L(2, 1)-labeling numbers of the four standard graph products and get significant improvements over the previously best known bounds for them. In Chapter 3 we study the L(2, 1)-labeling number of the composition of n graphs. We show that the L(2, 1)-labelling number of the composition of n graphs is much smaller than the square of the maximum degree. 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 K1,n-free graphs, where K1,n is the complete bipartite graph with one vertex in one side of the partition and n in the other. In Chapter 7 we obtain more results on L(2, 1)-labelings of the four standard graph products. 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." @default.
• W50590809 created "2016-06-24" @default.
• W50590809 creator A5006486369 @default.
• W50590809 date "2012-01-01" @default.
• W50590809 modified "2023-09-26" @default.
• W50590809 title "The Research on the L(2,1)-labeling problem from Graph theoretic and Graph Algorithmic Approaches" @default.
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• W50590809 hasPublicationYear "2012" @default.
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