Absorption cayley graph

Let R   be a commutative ring with two binary operators addition (+) and multiplication (.). Then ZnZn is a ring of integers modulo n, where n is a positive integer. A Absorption Cayley graph   denoted by Ω(Zn)Ω(Zn) is a graph whose vertex set is ZnZn, the integer modulo n and edge set E={ab:a+b∈S}E={ab:a+b∈S}, where S={a∈Zn:ab=ba=aS={a∈Zn:ab=ba=afor any  b∈Zn,b≠a,b≠1}b∈Zn,b≠a,b≠1}. Here ab=aab=a is the absorption property as b is absorbed in a. We study the characterization of Absorption cayley graphs along with its properties such as connectedness, degree, diameter, planarity, girth, regularity.