Inverse Planar Domination And Independent Planar Domination in Graphs

Abstract

Suppose that G is a simple, undirected, finite graph with no isolated vertices. A dominating set is said to be the planar dominating set if is a planar and dominating set such that all vertices in  have at least two adjacent vertices in . The planar domination number of is denoted by. In this paper, the inverse planar domination is introduced. In known graphs, such as the complete, complete bipartite, cycle, path, and others graphs, the inverse planar domination is computed. And study add condition to the planar dominating set to be independent set. Also, a possible application by the planar domination.