some aspects of unitary addition cayley graph of eisenstein integers modulo n

The unitary addition cayley graph gn[ω] of eisenstein integers modulo n has the vertex set en[ω], the set of eisenstein integers modulo n. any two vertices x = a1 + ωb1, y = a2 + ωb2 of gn[ω] are adjacent if and only if gcd(n (x + y), n) = 1, where n is the norm of any element of en[ω] given by n (a + ωb) = a² + b² − 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 mentionedgraph.