The bases of primitive non-powerful complete signed graphs
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The base of a signed digraph S is the minimum number k such thatfor 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 geq 3 the base of a primitive non-powerful signed complete graph K of order n is 2, 3 or 4.
Abstract
The base of a signed digraph S is the minimum number k such thatfor 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 geq 3 the base of a primitive non-powerful signed complete graph K of order n is 2, 3 or 4.
참고문헌 (5)
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- Q. Li, "Bounds on the kth multi-g base index of nearly reducible sign pattern matrices", Discrete Math, 308, pp.4846~4860 (2008)
- Y. Shao, "The local bases of non-powerful signed symmetric digraphs with loops", Ars. Combinatoria, 90, pp.357~369 (2009)
- L. You, "Bounds on the bases of irreducible generalized sign pattern matrices", Linear Algebra and Its Appl, 427, pp.285~300 (2007)