论文标题
签名图中的奇偶校验标签
Parity Labeling in Signed Graphs
论文作者
论文摘要
令$ s =（g，σ）$为签名图，其中$ g =（v，e）$是$ s $和$ s $的基础图，$ s $和$σ：令$ f：v（g）\ rightArrow \ {1,2，\ dots，| v（g）| \} $，以便$ f（uv）=+$ ifr，并且仅当$ f（u）$和$ f（u）$和$ f（v）$是同等的，$σ（uv）= $ f（uv）= - $ if（uv）= - 如果$ f（uv）= $ f（u）$ f（u）$ f（u）$ f（u）和$ f（u）和$ f（u）and pare ans pare as as parity。在$ f $下，我们得到签名的图形$ g_f $表示为$ s $，这是一个均等的图形。在本文中，我们在签名的图中启动了奇偶校验标签的研究，并在某些类别的签名图中定义并找到表示为$σ^ - （s）$的“ RNA”数字。我们还表征了一些签名的图形，这些图是奇偶校验签名的图。还提出了一些进一步研究的方向。
Let $S=(G, σ)$ be a signed graph where $G=(V, E)$ is a graph called the underlying graph of $S$ and $σ:E(G) \rightarrow \{+,~-\}$. Let $f:V(G) \rightarrow \{1,2,\dots,|V(G)|\}$ such that $σ(uv)=+$ if and only if $f(u)$ and $f(v)$ are of same parity and $σ(uv)=-$ if and only if $f(u)$ and $f(v)$ are of opposite parity. Under $f$ we get a signed graph $G_f$ denoted as $S$, which is a parity signed graph. In this paper, we initiate the study of parity labeling in signed graphs and we define and find `rna' number denoted as $σ^-(S)$ for some classes of signed graphs. We also characterize some signed graphs which are parity signed graphs. Some directions for further research are also suggested.
