Domination Number of Vertex Amalgamation of Graphs

Abstract

Abstract. For a graph G = (V, E), a subset S of V is called a dominating set if every vertex x in V is either in S or adjacent to a vertex in S. The domination number ( ) is the minimum cardinality of the dominating set of G. The dominating set of G with a minimum cardinality denoted by ( )-set. Let G1, G2, ... , Gt be subgraphs of the graph G. If the union of all these subgraphs is G and their intersection is {v}, then we say that G is the vertex-amalgamation of G1, G2, ... , Gt at vertex v. Based on the membership of the common vertex v in the ( )-set, there exist three conditions to be considered. First, if v elements of every ( )-set, second if there is no ( )-set containing v, and third if either v is element of ( )-set for ≤ ≤ or there is no ( )-set containing v for < ≤ . For these three conditions, the domination number of G as vertex-amalgamation of G1, G2, ... , Gt at vertex v can be determined.

Determination of bulog regional sub-division in east java using connected domination number theory

“…While in 1997, topics related to dominating number were developed namely connected dominating set [6]. Other research related to the dominating of the graph, such as Split Domination Number of Some Special Graphs [7,10] and Results Connecting Domination, Steiner and Steiner Domination Number of Graphs by Ramalakshmi and K. Palani [8]. The concept of connected dominating set is the suitable concept for Determination of Bulog Regional Sub-Divisions.…”