Rainbow game domination subdivision number of a graph

Abstract

The rainbow game domination subdivision number of a graph G is defined by the following game. Two players D and A, D playing first, alternately mark or subdivide an edge of G which is not yet marked nor subdivided. The game ends when all the edges of G are marked or subdivided and results in a new graph G'. . The purpose of D is to minimize the 2-rainbow dominating number \gamma_{r2}(G') of G' while A tries to maximize it. If both A and D play according to their optimal strategies,\gamma_{r2}(G') is well defined. We call this number the rainbow game domination subdivision number of G and denote it by \gamma_{r2}(G') . In this paper we initiate the study of the rainbow game domination subdivision number of a graph and present sharp bounds on the rainbow game domination subdivision number of a tree.

Keywords

• rainbow domination number
• rainbow game domination subdivision number