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SOME CHARACTERIZATION OF COMPLEMENTARY TRIPLE CONNECTED DOMINATION NUMBER OF 3 – REGULAR GRAPHS

Abstract

A graph is said to be triple connected if any three vertices lie on a path in G. A subset S of V of a nontrivial graph G is said to be complementary triple connected dominating set, if S is a dominating set and the induced sub graph <V-S> is triple connected. The minimum cardinality taken over all complementary triple connected dominating sets is called the complementary triple connected domination number of G and is denoted by ϒctc (G). The minimum number of colours required to colour all the vertices such that adjacent vertices do not receive the same colour is called chromatic number χ(G). In this paper, we investigate 3 - regular graphs for which ϒctc (G)= X(G)=3.

MAHADEVAN G, IRAVITHUL BASIRA A AND SIVAGNANAM C

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