On the Powers of Signed Graphs

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 $\sigma :E\to \{1,-1\}$. 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

References in corpus (1)

• On Signed Distance in Product of Signed Graphs