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

• Eskander Ali Tishreen University
• Ahed Hassoon Tishreen University
Keywords: Schur ring, Isomorphism problem, CI-graph

### Abstract

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 $$Cay(H,S)$$.

### Metrics

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