Distance Closed Domatic Number of Graphs

V. Sangeetha, T.N. Janakiraman "Distance Closed Domatic Number of Graphs", *International Journal of Mathematics Trends and Technology (IJMTT). *V50(4):222-227 October 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

**Abstract**

In a graph G = (V, E), a set S V(G) is said to be a distance closed set if for each vertex u S and for each w V – S, there exists at least one vertex v S such that d (u, v) = dG(u, w). A dominating set S is said to be a Distance Closed Dominating (D.C.D) set if S is distance closed.The cardinality of a minimum distance closed dominating set of G is called the distance closed domination number of G and is denoted by γdcl(G). The definition and the extensive study of the distance closed dominating sets in graphs are studied in [6].In this paper,the distance closed domatic number of some special classes of graphs are studied.Also, a general algorithm to find the structure of graphs with a given domatic number is proposed.

**Reference**

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**Keywords**

Distance, eccentricity, radius, diameter, degree, paths, cycles, trees, self-centred graphs, complete graphs, complete bipartite graphs, regular graphs, distance closed dominating set, distance closed domination number, distance closed domatic number.