INDEPENDENT SET OF DIVISOR CAYLEY GRAPH

Let 𝑛 ≥1 be an integer and let 𝑆 be the set of divisors of 𝑛 other than 𝑛. Then the set 𝑆∗ = {𝑠, 𝑛 - 𝑠 / 𝑠 ∈ 𝑆 } is a symmetric subset of the group (𝑍𝑛,⊕), the additive abelian group of integers modulo 𝑛. The Cayley graph of (𝑍𝑛,⊕) associated with the above symmetric subset 𝑆∗ is called the divisor Cayley graph and it is denoted by 𝐺( 𝑍𝑛, 𝐷). That is, the graph G(Zn, D) is the graph whose vertex set is V = { 0,1,2,., n–1} and the edge set E is the set of all ordered pairs of vertices x, y such that either x – y  S*, or , y – x  S*. In this paper we study the independent set, independence number and chromatic number of the divisor Cayley graph 𝐺( 𝑍𝑛, 𝐷).