The primitive bases of the signed cyclic graphs
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The base l(S) of a signed digraph S is the maximumnumber k such that for any vertices u, v of S, there is a pair ofwalks of length k from u to v with different signs. A graph can beregarded as a digraph if we consider its edges as two-sided arcs. Asigned cyclic graph Cn is a signed digraph obtained from the cycle Cn by giving signs to all arcs. In this paper, we compute the baseof a signed cyclic graph Cn when Cn is neither symmetric nor anti-symmetric. Combining with previous results, the base of all signedcyclic graphs are obtained.
Abstract
The base l(S) of a signed digraph S is the maximumnumber k such that for any vertices u, v of S, there is a pair ofwalks of length k from u to v with different signs. A graph can beregarded as a digraph if we consider its edges as two-sided arcs. Asigned cyclic graph Cn is a signed digraph obtained from the cycle Cn by giving signs to all arcs. In this paper, we compute the baseof a signed cyclic graph Cn when Cn is neither symmetric nor anti-symmetric. Combining with previous results, the base of all signedcyclic graphs are obtained.
참고문헌 (7)
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