论符号图的幂

arXiv: Combinatorics Pub Date : 2020-09-22 DOI:10.22049/CCO.2021.27083.1193

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

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引用次数: 0

摘要

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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On the Powers of Signed Graphs

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.

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来源期刊

arXiv: Combinatorics

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