On solving sets of Cayley graphs over \(\mathbb{Z}_{p^{\alpha}}\)

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Eskander Ali
Ahed Hassoon


In this paper, we study the isomorphism problem of Cayley graphs over the group \(\mathbb{Z}_{p^{\alpha}}\). Where we define solving set of \(\Gamma=Cay(H,S)\) to be the set \(\mathbf{P}\) of all permutations on \(\mathbb{Z}_{p^{\alpha}}\) which satisfying the following condition: every Cayley graph \(\Gamma'\) over \(\mathbb{Z}_{p^{\alpha}}\) is isomorphic with \(\Gamma\) if and only if there exists \(g\in \mathbf{P}\) such that \(\Gamma^{g}=\Gamma'\). And, so we display a method that allows us to know if \(Cay(H,S)\) is CI -graph. And give us all Cayley graphs over \(\mathbb{Z}_{p^{\alpha}}\) which are isomorphic with \(Cay(H,S)\).

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How to Cite
Ali, E., & Hassoon, A. (2019). On solving sets of Cayley graphs over \(\mathbb{Z}_{p^{\alpha}}\). International Journal of Algebra and Statistics, 8(1-2), 35-42. https://doi.org/10.20454/ijas.2019.1559