Some properties of Cayley signed graphs on finite abelian groups

Abstract

Let $\Sigma =(\Gamma ,\sigma )$ is a signed graph(or sigraph in short), where $\Gamma$ is a underlying graph of $\Sigma$ and $\sigma :E⟶\{+,-\}$ is a function. Consider $\Gamma =Cay({\mathbb{Z}}_{p_1}\times {\mathbb{Z}}_{p_1^{{\alpha }_1}{p}_2^{{\alpha }_2}\dots p_k^{{\alpha }_k}},\Phi )$, where all $p_1,p_2,\dots ,p_k$ are distinct prime factors and $\Phi ={\phi }_{p_1}\times {\phi }_{p_1^{{\alpha }_1}{p}_2^{{\alpha }_2}\dots p_k^{{\alpha }_k}}$. For any positive integer $n$, ${\phi }_n=\{\ell |1\le \ell <n,\gcd (\ell ,n)=1\}$. Motivated by \cite{s14}, we will investigate balancing in $\Sigma$ and $L(\Sigma )$, clusterability and sign-compatibility of $\Sigma$.

References in corpus (1)

• Matrices in the Theory of Signed Simple Graphs