# On the powers of signed graphs

Document Type : Original paper

Authors

1 Department of Mathematics, Research Scholar, Central University of Kerala, Kasaragod, India.

2 Department of Mathematics, Associate Professor, Central University of Kerala, Kasaragod, India

3 Department of Mathematics, Associate Professor, K M M Government Women&#039;s College, Kannur, India.

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 the $n^{th}$ 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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#### References

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[4] T.V. Shijin, P. Soorya, K. Shahul Hameed, and K.A. Germina, On signed distance in product of signed graphs, (2021), communicated.