Korean J. Math.  Vol 21, No 1 (2013)  pp.55-62
DOI: https://doi.org/10.11568/kjm.2013.21.1.55

THE PRIMITIVE BASES OF THE SIGNED CYCLIC GRAPHS

Byeong Moon Kim, Byung Chul Song

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. 


Subject classification



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ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr