Korean J. Math. Vol. 22 No. 3 (2014) pp.491-500
DOI: https://doi.org/10.11568/kjm.2014.22.3.491

The bases of primitive non-powerful complete signed graphs

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Published: Sep 25, 2014
Keywords:
base, sign pattern matrix, complete graph,
Mathematics Subject Classification:
05C20, 15B35.

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Byung Chul Song
Gangneung-Wonju National University
Byeong Moon Kim
Gangneung-Wonju National University

Abstract

The base of a signed digraph S is the minimum 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. Let K be a signed complete graph of order n, which is a signed digraph obtained by assigning +1 or −1 to each arc of the n-th order complete graph Kn considered as a digraph. In this paper we show that for n≥3 the base of a primitive non-powerful signed complete graph K of order n is 2, 3 or 4.



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Supporting Agencies

This work was supported by the Research Institute of Natural Science of Gangneung-Wonju National University.

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