Efficient domination in circulant graphs

Efficient domination in circulant graphs

Results about wreath products of circulant graphs are used to construct infinitely many circulant graphswith efficient dominating setswhose elements need not be equally spaced in Zn. It is proved that if a circulant graph of large degree has an efficient dominating set, then either its elements are equally spaced, or the graph is the wreath product of a smaller circulant graph with an efficient...

Domination in Circulant Graphs

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...

Total Domination in Circulant Graphs

Cayley graph is a graph constructed out of a group Γ and a generating set A ⊆ Γ. When Γ = Zn, the corresponding Cayley graph is called as a circulant graph and denoted by Cir(n, A). In this paper, we attempt to find the total domination number of Cir(n, A) for a particular generating set A of Zn and a minimum total dominating set of Cir(n, A). Further, it is proved that Cir(n, A) is 2-total exc...

Minimum Chromaticity and Efficient Domination of Circulant Graphs

Effective solutions to problems encountered in networks are often based on whether the elementary set can be partitioned into classes according to some specific criteria. The chromatic number of a graph G(V,E) is the minimum number of colours needed to colour the vertices of G such that no two adjacent vertices have the same colour. An independent set D of G is called an efficient dominating se...

Vertex Domination Critical in Circulant Graphs