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- W3117307253 abstract "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 $ain mathbb{Z}_n^*$ for which $S = aR$. In this paper, we obtain many families of Type-2 isomorphic circulant graphs and new abelian groups. Type-2 isomorphism of circulant graphs is a new type of isomorphism, different from already known Adam's or Type-1 isomorphism and Type-2 isomorphic circulant graphs have the property that they are without $CI$-property. The main results are Theorems ref{d4} and ref{d7}. Using Theorem ref{d7} and Lemma ref{d9}, a list of new abelian groups, $(T2_{np^3,p}(C_{np^3}(R^{np^3,x+yp}_i)),~circ)$ are given in the annexure for $n$ = 1 to 5, $p$ = 3,5,7, $x$ = 1 to $p-1$, $y$ = 0 to $np-1$ and $p,np^3-pin R^{np^3,x+yp}_i$ and for $p$ = 11, $n$ = 1 to 2, $x$ = 1 to $p-1$, $y$ = 0 to $np-1$ and $p,np^3-pin R^{np^3,x+yp}_i$. For more clarity, a list, without using Lemma ref{d9}, is given in cite{vw0A} for $n$ = 1 to 5, $p$ = 3,5,7,11, $x$ = 1 to $p-1$, $y$ = 0 to $np-1$ and $p,np^3-pin R^{np^3,x+yp}_i$." @default.
- W3117307253 created "2021-01-05" @default.
- W3117307253 creator A5091859275 @default.
- W3117307253 date "2020-12-18" @default.
- W3117307253 modified "2023-09-27" @default.
- W3117307253 title "Families of Circulant Graphs Without CI-Property and More Abelian Groups" @default.
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