On Domination Topological Indices of Graphs
Hanan Ahmed, Anwar Alwardi, M. Ruby Salestina
Abstract
Topological indices and domination in graphs are the essential topics in the theory of graphs. A set of vertices D ⊆ V (G) is said to be a dominating set for G if any vertex v ∈ V - D is adjacent to some vertex u ∈ D. In this research work, we define a new degree of each vertex v ∈ V (G), called the domination degree of v and denoted by dd(v), along with this new degree some domination indices based on domination degree are introduced. We study some basic properties of the domination degree function. Exact values and bounds for domination Zagreb indices of some families of graphs including the join and corona product are obtained. Finally, we generalize the domination degree of the vertex and new general indices are defined.