THE EQUITABLE SPLIT DOMINATION OF SIMPLE GRAPHS

The complexity of networks can be made simple by splitting the structure into smaller clusters. The partition of such networks can also be studied with graph domination. A dominating set D of a graph is a subset having vertices that connects the graph by having adjacency with at least one vertex of the remaining vertex set V - D. The concept of split domination disconnects the graph into separated sub-graphs. For balanced splitting of smaller sub-graphs and to cover all the points in the whole network with identified dominant positions, the idea of equitable split domination is introduced and applied for graphs such as, path, cycle, prism, wheel and ladder.