I did Google search and can’t find a good answer. I thought I should ask experts here. Cayley graph is defined for groups. My question is: Is there a special name for the Cayley graph of semigroups?

Does it exist any program (for linux) which can generate a nice Cayley graph of any $\mathbb Z_n$? (If it’s possible to create such a graph at all, that is.) (where perhaps $n ≤ 100$ or something like that)

Consider the following problem Let $n \leq 5$ and let $\Gamma = \mathrm{Cay}(C_{2n},S)$ be the Cayley graph with Cayley set $S$. Show that $\Gamma$ is isomorphic to $\mathrm{Cay}(D_{2n},S’)$ for a suitable $S’.$ Recall that $\Gamma = \mathrm{Cay}(G,S)$ is a Cayley graph with vertex set $G$ if $G$ is a group, $S$ is a subset of […]

How we can make Cayley graph on $ D_{2n} $ and $ \mathbb Z_n$? What can be S in $Cay(D_{2n},S)$ and $ Cay(\mathbb Z_n ,S)$, Please write one example. Thanks for advise.

How can I show that the Petersen graph is not a Cayley graph? I don’t know very much about Cayley graphs, I know that they are vertex-transitive, but so is the Petersen graph. It probably has to do with the group structure of $\Gamma$ in $Cay(\Gamma,S)$ (which is a group of order $10$, i.e., it […]

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