论文标题
卡利（Cayley
Some properties of Cayley signed graphs on finite abelian groups
论文作者
论文摘要
让$σ=（γ，σ）$是签名的图（或简称Sigraph），其中$γ$是$σ$和$σ的基础图：考虑$γ= cay（\ Mathbb {z} _ {p_ {p_ {1}} \ times \ mathbb {z} _ {p_ {p_ {1}^{α_{1}}} φ）$，其中所有$ p_ {1}，p_ {2}，\ ldots，p_ {k} $都是不同的素数因素，$φ=φ__{p_ {1}}} \timesφ__{p_ {p_ {p_ {1}^{α_{α_{1}} p_ {k}^{α_{k}}} $。对于任何正整数$ n $，$φ_{n} = \ {\ ell | 1 \ leq \ ell <n，\ gcd（\ ell，n）= 1 \} $。由\ cite {s14}激励，我们将调查$σ$和$ l（σ）$，clusterable和$σ$的标志兼容性的平衡。
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 $Σ$.
