Domination Numbers, Chromatic Numbers and Total Domination Numbers of all Powers of Cycles using a Circular-Arc Graph G

Abstract

Graph theory is the study of graphs, which are mathematical structures used to demonstrate pair wise relations between objects. A dominating set is used as a backbone for communication. Among various applications of the theory of domination, chromatic number and total domination the most often discussed is a communication network. The Circular-arc graphs have drawn the attention of research for over number of years. They are extensively studied and revealed their practical relevance for modeling problems arising in the real world. The aim of this paper is to find the domination numbers, Chromatic numbers and Total domination numbers of all powers of cycles using a Circular-arc graph G corresponding to a Circular-arc family A.