On Partition Dimension and Domination of Abid-Waheed 〖(AW)〗_r^4 Graph

Abstract

A graph denoted by H, which has a simple link between its vertices, possesses the set of vertices V(H) . Given a graph, a set that is dominant, is a subset of vertex set such that any vertex outside of is close to at least one vertex inside of . The smallest size of for the dominating set is known as the graph’s domination number. When a linked graph H has a vertex x and a subset of the vertex set, the separation between x and S is given by. Pertaining to an ordered k-partition of , the illustration of in relation to Π is to be the k-vectorAbid-Waheed graph is a simply connected graph which contains vertices and edges for all and In this paper, we studied some results on the domination number, independent and restrained domination number denoted by respectively in the Abid-Waheed graphs and the relation between domination number, independent and restrained domination number. Also, the objective of this paper is to generate a partition dimension of.

Keywords

• Abid-Waheed Graph, Domination, Independent Domination, Partition Dimension, Restrained Domination.