Let H be a subset of a commutative graded ring R. The Cayley graph Cay(R,H) is a graph whose vertex set is R and two vertices a and b are adjacent if and only if a−b∈H. The Cayley sum graph Cay+(R,H) is a graph whose vertex set is R and two vertices a and b are adjacent if and only if a+b∈H. Let S be the set of homogeneous elements and Z(R) be the set of zero-divisors of R. In this paper, we study Cay+(R,Z(R)) (total graph) and Cay(R,S). In particular, if R is an Artinian graded ring, we show that Cay(R,S) is isomorphic to a Hamming graph and conversely any Hamming graph is isomorphic to a subgraph of Cay(R,S) for some finite graded ring R. Read More: https://www.worldscientific.com/doi/abs/10.1142/S0219498818501165
