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'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

[1] J. Akiyama, H. Era, and G. Exoo, Further results on graph equations for line graphs and n-th power graphs, Discrete Math. 34 (1981), no. 3, 209–218.
[2] F. Harary, A characterization of balanced signed graphs, Mich. Math. J. 2 (1953), 143–146.
[3] K. Shahul Hameed, T.V. Shijin, P. Soorya, K.A. Germina, and T. Zaslavsky, Signed distance in signed graphs, Linear Algebra Appl. 608 (2021), 236–247.
[4] T.V. Shijin, P. Soorya, K. Shahul Hameed, and K.A. Germina, On signed distance in product of signed graphs, (2021), communicated.
Communications in Combinatorics and Optimization
Volume 7, Issue 1
June 2022
Pages 45-51

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