On the Powers of Signed Graphs

T. Shijin, A. GerminaK., K. ShahulHameed
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Abstract

A signed graph is an ordered pair $\Sigma=(G,\sigma),$ where $G=(V,E)$ is the underlying graph of $\Sigma$ with a signature function $\sigma:E\rightarrow \{1,-1\}$. In this article, we define $n^{th}$ power of a signed graph and discuss some properties of these powers of signed graphs. As we can define two types of signed graphs as the power of a signed graph, necessary and sufficient conditions are given for an $n^{th}$ power of a signed graph to be unique. Also, we characterize balanced power signed graphs.
论符号图的幂
签名图是一个有序对$\Sigma=(G,\sigma),$,其中$G=(V,E)$是具有签名函数$\sigma:E\rightarrow \{1,-1\}$的$\Sigma$的底层图。在本文中,我们定义了$n^{th}$符号图的幂,并讨论了符号图的幂的一些性质。由于我们可以将两种类型的签名图定义为签名图的幂,因此给出了签名图$n^{th}$幂唯一的充分必要条件。此外,我们描述了平衡幂符号图。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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