Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs

Abstract

Given a graph $G=(V,E)$, the subdivision of an edge $e=uv\in E(G)$ means the substitution of the edge $e$ by a vertex x and the new edges $ux$ and $xv$. The domination subdivision number of a graph $G$ is the minimum number of edges of $G$ which must be subdivided (where each edge can be subdivided at most once) in order to increase the domination number. Also, the domination multisubdivision number of $G$ is the minimum number of subdivisions which must be done in one edge such that the domination number increases. Moreover, the concepts of paired domination and independent domination subdivision (respectively multisubdivision) numbers are defined similarly. In this paper we study the domination, paired domination and independent domination (subdivision and multisubdivision) numbers of the generalized corona graphs.