Notions of domination for some classses of graphs

Date of Publication

2015

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Leonor Aquino Ruivivar

Abstract/Summary

If G = (V E) is a nite simple connected graph, a subset S of V is said to be a dominating set of the graph G if every vertex of G is either in S or is adjacent to at least one element of S. The minimum cardinality of a dominating set of G is called the domination number of G. In the present study, we considered variations of the concept of domination in a graph.

Specifically, we looked into triple connected dominating sets and triple connected complementary tree dominating sets of a connected nite simple undirected graph, and the domination parameters of the triple connected domination number and triple connected complementary tree domination number. Conditions for the existence of such dominating sets, and bounds for the corresponding domination parameters, were identified. We also determined the exact values of these parameters for certain classes of graphs, and the relationship of these domination parameters with other graph parameters such as the chromatic number, connectivity, and maximum vertex degree.

Abstract Format

html

Language

English

Format

Electronic

Accession Number

CDTU021092

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Keywords

Graph theory; Domination (Graph theory)

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