In this paper, we continue the study of the total domination game in graphs introduced in [Graphs Combin. 31(5) (2015), 1453–1462], where the players Dominator and Staller alternately select vertices of G. Each vertex chosen must strictly increase the number of vertices totally dominated, where a vertex totally dominates another vertex if they are neighbors. This process eventually produces a t...

Let GG =(V,E)(V,E) be a simple graph. A subset SS is said to Semi-Strong if for every vertex vv in VV, |N(v)∩S|≤1|N(v)∩S|≤1, or no two vertices of have the same neighbour that is, are joined by path length VV. The minimum cardinality semi-strong partition called chromatic number and denoted χsGχsG. proper colour dominator dominates some class, , adjacent with element class. In this paper, inste...