On the Powers of Signed Graphs

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