Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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THE PRIMITIVE BASES OF THE SIGNED CYCLIC GRAPHS

  • Received : 2013.01.02
  • Accepted : 2013.02.15
  • Published : 2013.03.30
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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 $C_n$ 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 antisymmetric. Combining with previous results, the base of all signed cyclic graphs are obtained.

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References

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