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For a postive integer $n$ and a subset $S$ of $\mathbb{Z}_n$, let$\left\langle S\right\rangle =\mathbb{Z}_n$, and $w:S\rightarrow\mathbb{N}$ bea function. The weighted Cayley graph of the cyclic group $\mathbb{Z}_n$ withrespect to $S$ and $w$ is denoted by $C_n(S,w)$. We give an explicitdescription of the Grothendieck group of the Leavitt path algebras of$C_n(S,w)$. We also give description of Leavitt path algebras of $C_n(S,w)$ insome special cases.

Leavitt path algebras of weighted Cayley graphs $C_n(S,w)$