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- W3173344002 abstract "Circulant graphs $C_n(R)$ and $C_n(S)$ are said to be emph{Adam's isomorphic} if there exist some $ain mathbb{Z}_n^*$ such that $S = aR$. 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 $S = aR.$ Vilfred cite{v20} defined and studied Type-2 circulant graph isomorphism, a new type of isomorphism different from Adam's isomorphism and without $CI$-property and we obtained families of isomorphic circulant graphs of Type-2 with respect to $r$ = 2,3,5,7 cite{v20}, cite{vw1} - cite{vw3}. In this paper, we obtain new families of Type-2 isomorphic circulant graphs with respect to $r = p$ and of order $np^3$ and new abelian groups on these isomorphic graphs where $p$ is a prime number and $ninmathbb{N}$. Theorems 4.2 and 4.4 are the main results. Using Theorem 4.4, 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 $p$ = 3,5,7,11 and $n$ = 1 to 5 and also for $p$ = 13 and $n$ = 1 to 3, $1 leq x leq p-1$ and $0 leq y leq np-1$, $p,np^3-pin R^{np^3,x+yp}_i$ where $T2_{np^3,p}(C_{np^3}(R^{np^3,x+yp}_i))$ = ${C_{np^3}(R^{np^3,x+yp}_i):~ i = 1$ to $p}$ is a set of Type-2 isomorphic circulant graphs $C_{np^3}(R^{np^3,x+yp}_i)$ with respect to $r = p = gcd(np^3, p)$, $1 leq i leq p$." @default.
- W3173344002 created "2021-07-05" @default.
- W3173344002 creator A5091859275 @default.
- W3173344002 date "2020-12-18" @default.
- W3173344002 modified "2023-09-27" @default.
- W3173344002 title "On New Type of Isomorphic Circulant Graphs of Order $np^3$ and New Groups" @default.
- W3173344002 hasPublicationYear "2020" @default.
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