THE PRIMITIVE BASES OF THE SIGNED CYCLIC GRAPHS

Abstract. The base l(S) of a signed digraph S is the maximum 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. A graph can be regarded as a digraph if we consider its edges as two-sided arcs. A signed cyclic graph fCn is a signed digraph obtained from the cycle Cn by giving signs to all arcs. In this paper, we compute the base of a signed cyclic graph fCn when fCn is neither symmetric nor anti-symmetric. Combining with previous results, the base of all signed cyclic graphs are obtained. 1