In this paper, we continue the study of the domination game in graphs introduced by Brešar, Klavžar, and Rall [SIAM J. Discrete Math. 24 (2010) 979–991]. We study the total version of the domination game and show that these two versions differ significantly. We present a key lemma, known as the Total Continuation Principle, to compare the Dominator-start total domination game and the Staller-st...

In this paper, the concept of incidence domination number of graphs  is introduced and the incidence dominating set and  the incidence domination number  of some particular graphs such as  paths, cycles, wheels, complete graphs and stars are studied.