Total Domination in Certain Nanotori

Indra Rajasingh1, R. Jayagopal1, R. Sundara Rajan2
1School of Advanced Sciences, Vellore Institute of Technology, Chennai, India
2Department of Mathematics, Hindustan Institute of Technology and Science, Chennai, India

Abstract

A set \(S\) of vertices in a graph \(G\) is said to be a dominating set if every vertex in \(V(G)\S\) is adjacent to some vertex in \(S\). A dominating set \(S\) is called a total dominating set if each vertex of \(V(G)\) is adjacent to some vertex in \(S\). Molecules arranging themselves into predictable patterns on silicon chips could lead to microprocessors with much smaller circuit elements. Mathematically, assembling in predictable patterns is equivalent to packing in graphs. In this pa-per, we determine the total domination number for certain nanotori using packing as a tool.

Keywords: Domination, Total domination, H-packing, Perfect packing, Nanotori