Some aspects of unitary addition Cayley graph of Eisensteinintegers modulo \textit{n}

The unitary addition Cayley graph G_n[\omega] of Eisenstein integers modulo n has the vertex set \mathbb{E}_n[\omega], the set of Eisenstein integers modulo n. Any two vertices x=a_۱+\omega b_۱, y=a_۲+\omega b_۲ of G_n[\omega] are adjacent if and only if gcd(N(x+y),n)=۱, where N is the norm of any element of \mathbb{E}_n[\omega] given by N(a+\omega b)=a^۲+b^۲-ab. In this paper we obtain some basic graph invariants such as degree of the vertices, number of edges, diameter, girth, clique number and chromatic number of unitary addition Cayley graph of Eisenstein integers modulo n. This paper also focuses on determining the independence number of the above mentioned graph. 

Keywords:

Eisenstein integers , diameter , girth , Clique number , chromatic number , Independence number , Unitary addition Cayley graph