Notions of domination for some classses of graphs

• Main Authors: Castaneda, Adrian Timothy S., Medina, Matthew Ayemart S.
• Format: text
• Language: English
• Published: Animo Repository 2015
• Subjects: Graph theory; Domination (Graph theory); Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/18387
• Institution: De La Salle University

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.