Distance Closed Domatic Number of Graphs International Journal of Mathematics Trends and Technology (IJMTT) © 2017 by IJMTT Journal Volume-50 Number-4 Year of Publication : 2017 Authors : V. Sangeetha, T.N. Janakiraman 10.14445/22315373/IJMTT-V50P536 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 .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.

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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.