Domination in Circulant Graphs

2-Tuple Total Domination Number in Circulant Graphs

In this paper, a necessary and sufficient condition for the existence of an efficient 2-dominating set in a class of circulant graphs has been obtained and for those circulant graphs, an upper bound for the 2domination number is also obtained. For the circulant graphs Cir(n,A), where A = {1, 2, . . . , x, n − 1, n − 2, . . . , n − x} and x ≤ bn−1 2 c, the perfect 2-tuple total domination number...

Vertex Domination Critical in Circulant Graphs

Locating -Total Domination in Circulant Graphs

A locating-total dominating set (LTDS) S of a graph G is a total dominating set S of G such that for every two vertices u and v in V(G) − S, N(u)∩S ≠ N(v)∩S. The locating-total domination number ( ) l t G  is the minimum cardinality of a LTDS of G. A LTDS of cardinality ( ) l t G  we call a ( ) l t G  -set. In this paper, we determine the locating-total domination number for the special clas...

On the Distance Paired-Domination of Circulant Graphs

Let G = (V, E) be a graph without isolated vertices. A set D ⊆ V is a d-distance paired-dominating set of G if D is a d-distance dominating set of G and the induced subgraph 〈D〉 has a perfect matching. The minimum cardinality of a d-distance paired-dominating set for graph G is the d-distance paired-domination number, denoted by γd p(G). In this paper, we study the ddistance paired-domination n...

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...