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http://dx.doi.org/10.11568/kjm.2013.21.1.55

THE PRIMITIVE BASES OF THE SIGNED CYCLIC GRAPHS  

Kim, Byeong Moon (Department of Mathematics Gangneung-Wonju National University)
Song, Byung Chul (Department of Mathematics Gangneung-Wonju National University)
Publication Information
Korean Journal of Mathematics / v.21, no.1, 2013 , pp. 55-62 More about this Journal
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.
Keywords
base; sign pattern matrix; directed cycle;
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