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On the Powers of Signed Graphs

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2020Embargo end date: 01 Jan 2020Publisher:arXiv

Authors: Germina K A; Shahul Hameed K; Shijin T V;

doi: 10.48550/arxiv.2009.10486 , 10.22049/cco.2021.27083.1193

arXiv: http://arxiv.org/abs/2009.10486

On the Powers of Signed Graphs

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Abstract

A signed graph is an ordered pair $��=(G,��),$ where $G=(V,E)$ is the underlying graph of $��$ with a signature function $��:E\rightarrow \{1,-1\}$. 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.

10 pages, 1 figure

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Keywords

05C12, 05C22, 05C50, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)

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