DOMINATING SETS OF UNITARY DIVISOR CAYLEY GRAPHS

Let n
1 be an integer and S be the set of unitary symmetric subset of the group (Zn, ⊕ associated with the above symmetric subset S* is called the Unitary Divisor Cayley .That is, G(Zn, Un) is the graph whose vertex set Let G (V, E) be a graph. A subset D of V is said to be a dominating set of G if every in D. A dominating set with minimum cardinality is ca domination number of G and is denoted by KEYWORDS: Unitary Divisor Cayley Graph 1. INTRODUCTION Berge [4] and Ore [12] are the first to introduce the to the theory of domination in graphs. “optimal domination in graphs”. They were the first to use the notatio which subsequently became the accepted notation. Allan and Laskar [1], Cockayne and Hedetniemi [6], Arumugam [3], Sam path Kumar [13] and others have contributed significantly to the theory of dominating sets and d An introduction and an extensive overview on domination in graphs and related topics are given by Haynes et al. [8]. In the sequel edited by Haynes, Hedetniemi and Slater [9], several authors presented a survey of articles in t domination in graphs. Cockayne, C.J et.al The applications of both domination and total domination are widely used in Networks. In this chapter, we discuss dominating sets and total dominating sets of Unitary Here we have presented an algorithm which finds all minimal dominating and total dominating This algorithm finds all closed and open neighborhood sets respectively which cover all the vertices of G (Z illustrated for different values of n. 2. DOMINATING SETS OF UNITARY DIVISOR CAYLEY GRAPH Let us define a dominating set as follows Definition Let G (V, E) be a graph. A subset D of V is said to be a dominating set of G if every a vertex in D. International Journal of Applied Mathematics & Statistical Sciences (IJAMSS) ISSN(P): 2319-3972; ISSN(E): 2319-3980 Vol. 6, Issue 5, Aug – Sep 2017; 19-42 © IASET G. MIRONA & B. MAHESWAR Mathematics, Sri Padmavati Womens University, Tirupati, Andhra Pradesh, India divisors of n.Then the set S*= {s, n ), the additive abelian group of integers modulo n. The Cayley graph of (Zn, graph and it is denoted by G(Zn, Un) is V= {0,1,2,…, n-1} and the edge set is E = {(x vertex in V called a minimum dominating set and its cardinality is called the ϒ (G).