*Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram, Dindigul
**Research Scholar, Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram, Dindigul
***Department of General Requirements, College of Applied Sciences-Ibri, Sultanate of Oman
In this paper, we introduce the concept of nonsplit perfect triple connected domination number of a graph. A subset S of V of a non trivial graph G is said to be nonsplit perfect triple connected dominating set if S is a triple connected dominating set and <V−S>is connected and has at least one perfect matching. The minimum cardinality taken over all nonsplit perfect triple connected dominating sets in G is called the nonsplit perfect triple connected domination number of G and is denoted by (G). We initiate to study this parameter and investigate its relationship with chromatic number.
Domination number, nonsplit perfect triple connected domination number and chromatic number
