Upper whole domination in a graph

Abstract

The new parameters of domination in graphs are being initiated that are the upper whole domination and its inverse. Many properties and theorems about the upper whole dominations number have been discussed. Also, it is determined to certain graphs as a cycle, complete, path, wheel, and complete bipartite with some properties. Finally, most properties of inverse upper domination number have been studied. Furthermore, determined this definition of certain graphs are been mentioned above.

Subject Classification:

• 05C69

Keywords:

• Whole dominating set
• Upper whole domination number and inverse upper whole domination number