A survey on variant domination problems in geometric intersection graphs (Q6536206)

A graph \(G=(V,E)\) is called a geometric intersection graph if there exists a set \(P\) of geometric objects and a bijection \(f:V\rightarrow P\) such that \(uv\in E\) if and only if \(f(u)\) and \(f(v)\) intersect. If \(P\) is a set of discs, then \(G\) is called a disc graph. Other types of geometric intersection graphs are unit disc graphs, rectangle graphs and unit square\Ngraphs. In this paper, the authors present a survey of complexity, algorithmic results, and approximation algorithm results for several variants of domination problems such as minimum domination problem, minimum connected domination problem, minimum total domination problem, minimum total restrained domination problem, minimum secure domination problem, minimum secure connected domination problem and minimum secure total domination problem in some geometric intersection graphs such as disc graphs, rectangle graphs, unit disc graphs, and circle graphs. Several open problems and directions for further research are presented in the concluding section.