The bases of primitive non-powerful complete signed graphs
The base of a signed digraph $S$ is the minimum number $k$ such that for any vertices $u$, $v$ of $S$, there is a pair of walks of length $k$ from $u$ to $v$ with different signs. Let $K$ be a signed complete graph of order $n$, which is a signed digraph obtained by assigning $+1$ or $-1$ to each arc of the $n$-th order complete graph $K_n$ considered as a digraph. In this paper we show that for $n \geq 3$ the base of a primitive non-powerful signed complete graph $K$ of order $n$ is $2$, $3$ or $4$.
Subject classification05C20, 15B35.
Sponsor(s)This work was supported by the Research Institute of Natural Science of Gangneung-Wonju National University.
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