## ON SOME RESULTS OF PERFECT DOMINATIONS OF SOME GRAPHS

## ON SOME RESULTS OF PERFECT DOMINATIONS OF SOME GRAPHS

*M. L. Caay, S. R. Palahang*

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## Abstract

A dominating set D V (G) of a simple graph G is the set of all u such that for every v 2 V (G)nD, uv 2 E(G). An independent set I V (G) is a set of non-adjacent vertices in G. An independent dominating set Di V (G) is a subset of V (G) that is both independent set and dominating set. A subset S of V (G) is called a perfect dominating set of S if for each v belongs to V (G)nS, there exists a unique element u 2 S, such that v and u are adjacent. De ne an independent perfect dominating set Dip of G to be a dominating set that is both independent dominating set and perfect dominating set. The minimum cardinality of an independent perfect dominating set of G is called an independent perfect domination number of G, denoted by ip(G). If a graph has a perfect dominating set, we say that the graph G is ip-graph. In this study, we determine some bounds and parameters of the graph as well as the existence existence of this invariant to some graphs and graphs formed by some binary operations.

## Keywords

perfect dominating set, independent dominating set, independent perfect dominating set, independent perfect domination number.