Open Access Journal

ISSN : 2456-1304 (Online)

International Journal of Engineering Research in Electronics and Communication Engineering(IJERECE)

Monthly Journal for Electronics and Communication Engineering

Open Access Journal

International Journal of Science Engineering and Management (IJSEM)

Monthly Journal for Science Engineering and Management

ISSN : 2456-1304 (Online)

A Study on Restrained Triple Connected Two Domination Number of a Graph

Author : Dr. A.Punitha Tharani 1 A.Robina Tony 2

Date of Publication :6th February 2018

Abstract: The concept of triple connected graphs with real life application was introduced by considering the existence of a path containing any three vertices of a graph G. Mahadevan et. al., introduced the concept of triple connected domination number of a graph. In this paper, we introduce a new domination parameter, called restrained triple connected two domination number of a graph. A subset S of V of a non – trivial graph G is said to be a restrained triple connected two dominating set, if S is a restrained two dominating set and the induced subgraph is triple connected. The minimum cardinality taken over all restrained triple connected two dominating sets is called the restrained triple connected two domination number of G and is denoted by γ2rtc(G). Any restrained triple connected two dominating set with γ2rtc vertices is called a γ2rtc- set of G. We determine this number for some standard and special graphs and obtain bounds for general graph. Its relationship with other graph theoretical parameters is also investigated

Reference :

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    2. J. Jagan Mohana , Indrani Kelkarb, Restrained 2-Domination Number of Complete Grid Graphs, International Journal of Applied Mathematics and Computation Journal, ISSN: 0974 - 4665 (Print) 0974 - 4673 (Online) Volume 4(4) 2012 352–358.
    3.  V.R.Kulli, College Graph Theory, Vishwa International Publications, Gulbarga, India (2012).
    4. V.R.Kulli, Theory of Domination in Graphs, Vishwa International Publications, Gulbarga, India (2010)
    5. V.R.Kulli and S.C.Sigarakanti, The connected edge domination number of a graph, Technical Report 8801, Dept Math. Gulbarga University, (1988).
    6. G. Mahadevan, A. Selvam, J. Paulraj Joseph and, T. Subramanian, Triple connected domination number of a graph, International Journal of Mathematical Combinatorics, Vol.3 (2012), 93 - 104. 

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