Abstract

On the Variants of Domination Number of Certain Graphs

S. Sarah Surya and Fathima Sana Afrin. S

Department of Mathematics, Stella Maris College (Autonomous), Chennai-600 086, INDIA.

ABSTRACT

Domination in graphs has applications to several fields. A Dominating set for a graph 𝐺=(𝑉,𝐸) is a subset 𝑆 of 𝑉 such that every vertex not in 𝑆 is adjacent to at least one member of S. The domination number 𝛾(𝐺) is the number of vertices in a smallest dominating set for G. In this paper, we determine some parameters of domination namely, the total domination number and independent domination number for certain graphs like the Mongolian tent, Frock graph, Extended fully connected cubic network and we also obtain the domination number for the generalized web graph 𝑊(𝑡,3),𝑊(𝑡,4)where 𝑡≥4.

Keywords :Domination number, total domination number, independent domination number, Mongolian tent, Frock graph, Extended fully connected cubic network, generalized web graph.

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