A Survey on Variant Domination Problems in Geometric Intersection Graphs.

Given a graph G with vertex set V , a subset S of V is called a dominating set of G if every vertex is either in S or is adjacent to a vertex in S. There are a lot of variants for dominating sets, such as connected dominating sets, total dominating sets, total restricted dominating sets, secure (connected, total) dominating sets, etc. Geometric intersection graphs are graphs for which there is a bijection b between the vertices and a set P of geometric objects (for example, disks, rectangles, etc.) such that there is an edge between two vertices v and w if and only if the objects b (v) and b (w) intersect. In this paper, we offer a survey about complexity and algorithmic results on variant domination problems in geometric intersection graphs. [ABSTRACT FROM AUTHOR]