Domination Number in the Context of Some New Graphs

Abstract

Let G = (V, E) be a graph, where D is a subset of V, such that the set of vertices in the set (V-D) is adjacent to at least one vertex in set D. Then, set D is known as the domination set. In other words, a dominating set in graph G is a set of vertices S, such that every vertex in the graph either belongs to S or is adjacent to at least one vertex in S. In this paper, we investigate the domination number for some different types of graphs like antiprism graph An, alternate pentagonal snake A(PSn), cycle with one chord, and m-copies of cycle Cn with one chord. The domination number is frequently employed in computer science for tasks such as to optimize network design, algorithm design, security analysis, etc. Complex computational and network related challenges can be solved by domination number.

Keywords

• domination number
• domination set
• antiprism graph A_n
• alternate pentagonal snake A(PS_n)
• cycle with one chord
• m-copies of cycle C_n with one chord