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 \tilde{C_n} is a signed digraph obtained from the cycle n C_n by giving signs to all arcs. In this paper, we compute the base of a signed cyclic graph \tilde{C_n} when \tilde{C_n} is neither symmetric nor anti-symmetric. Combining with previous results, the base of all signed cyclic graphs are obtained.