## DOMINATION NUMBER IN UNIT DISK GRAPH: VIA S- CLIQUE APPROACH

M. GHANBARI *

Department of Mathematics, Tafresh University, Tafresh, Iran

D. A. MOJDEH

Department of Mathematics, Tafresh University, Tafresh, Iran and Department of Mathematics, University of Mazandaran, Babolsar, Iran

M. RAMEZANI

Department of Mathematics, Tafresh University, Tafresh, Iran

*Author to whom correspondence should be addressed.

### Abstract

Let *G* = (*V,E*) be a graph with vertex set* V *= *V* (*G*) and edge set *E* = *E*(*G*). For a positive integer *s*, a subset of vertices *K*is called an *s*-clique if for any *u*, *v ∈ K *we have *d*(*u, v*) ≤ *s*. Namely, an *s*-clique is a subset of nodes with pairwise distance at most s in the graph. A subset *S* ⊆ *V* of vertices in a graph is called a dominating set if every vertex is either in the subset *S* or adjacent to a vertex *S*. The size of the minimum dominating set in a graph *G* is called the domination number, denoted by γ(*G*). This study is concentrated on distance based clique relaxations in unit disk graphs arising in wireless networking applications. Although, computing the minimum dominating set is NP-hard even in unit disk graphs; but as a simple approach, the domination number of unit disk graph is approximated by *s*-cliques.

Keywords: Unit disk graph, domination number, s-clique

#### How to Cite

*Asian Journal of Mathematics and Computer Research*,

*7*(3), 237–244. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/411