Some properties of Cayley signed graphs on finite abelian groups
Let $Σ=(Γ, σ)$ is a signed graph(or sigraph in short), where $Γ$ is a underlying graph of $Σ$ and $σ:E\longrightarrow \{+, -\}$ is a function. Consider $Γ=Cay(\mathbb{Z}_{p_{1}}\times \mathbb{Z}_{p_{1}^{α_{1}}p_{2}^{α_{2}} \ldots p_{k}^{α_{k}}}, Φ)$, where all $p_{1}, p_{2}, \ldots, p_{k}$ are distinct prime factors and $Φ=φ_{p_{1}}\timesφ_{p_{1}^{α_{1}}p_{2}^{α_{2}} \ldots p_{k}^{α_{k}}}$. For any positive integer $n$, $φ_{n}=\{\ell| 1\leq \ell<n, \gcd(\ell, n)=1\}$. Motivated by \cite{s14}, we will investigate balancing in $Σ$ and $L(Σ)$, clusterability and sign-compatibility of $Σ$.
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