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

Byung Chul Song, Byeong Moon Kim

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 $K_n$ considered as a digraph. In this paper we show that for $n \geq 3$ the base of a primitive non-powerful signed complete graph $K$ of order $n$ is $2$, $3$ or $4$.


Keywords


base, sign pattern matrix, complete graph,

Subject classification

05C20, 15B35.

Sponsor(s)

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

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References


Y. Gao and Y. Huang and Y. Shao, Bases of primitive non-powerful signed symmetric digraphs with (Google Scholar)

loops, Ars. Combinatoria, 90, 383-388 (2009). (Google Scholar)

B. Li, F. Hall and J. Stuart, Irreducible powerful ray pattern matrices, Linear Algebra and Its Appl., (Google Scholar)

, 47-58 (2002). (Google Scholar)

Q. Li and B. Liu, Bounds on the kth multi-g base index of nearly reducible sign pattern matrices, (Google Scholar)

Discrete Math., 308, 4846-4860 (2008). (Google Scholar)

Y. Shao and Y. Gao, The local bases of non-powerful signed symmetric digraphs with loops, Ars. (Google Scholar)

Combinatoria, 90, 357-369 (2009). (Google Scholar)

L. You, J. Shao and H. Shan, Bounds on the bases of irreducible generalized sign pattern matrices, (Google Scholar)

Linear Algebra and Its Appl., 427, 285-300 (2007). (Google Scholar)


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