Domination in Circulant Graphs
Nader Jafari Rad · 2009
A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G − v is less than the total domination number of G. We call these graphs γt-critical. In this paper, we determine the domination and the total domination number in the Circulant graphs Cn〈1, 3〉, and then study γ-criticality and γt-criticality in these graphs. Finally, we provide answers to some open questions. 1