Vertex Domination Critical in Circulant Graphs

Abstract

A graph G is vertex domination critical if for any vertex v of G, the domination number of G – v is less than the domination number of G. We call these graphs γ-critical if domination number of G is γ. In this paper, we determine the domination and the total domination number of Cir(n,A) for two particular generating sets A of Zn, and then study γ-critical in these graphs.