New Families of Circulant Graphs Without Cayley Isomorphism Property with ri=2

A circulant graph C n ( R ) is said to have the Cayley isomorphism ( CI ) property if whenever C n ( S ) is isomorphic to C n ( R ) , there is some a ∈ Z n ∗ for which S = a R . In this paper, we define Type-2 isomorphism, a new type of isomorphism of circulant graphs, different from already known Adam’s isomorphism, with r i = 2 and present its properties. At the end of the paper, we present a VB program to show the action of the transformation acting on C n ( R ) to obtain Type-2 isomorphism. Type-2 isomorphic circulant graphs have the property that they are isomorphic circulant graphs without CI - property .