June 10, 2023
Doost Ali Mojdeh

Doost Ali Mojdeh

Degree: Professor
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Education: Ph.D in Mathematics (Graph Theory and Combinatorics)
Phone: 011-35302448
Faculty: Faculty of Mathematical Sciences

Research

Title DOMINATION NUMBER IN UNIT DISK GRAPH: VIA S- CLIQUE APPROACH
Type Article
Keywords
Unit disk graph, domination number, s-clique
Journal Asian Journal of Mathematics and Computer Research
DOI
Researchers Mojtaba Ghanbari (First researcher) , Doost Ali Mojdeh (Second researcher) , Mehdi Ramezani (Third researcher)

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.