Base of the Non-powerful Signed Tournament
نویسندگان
چکیده
A signed digraph S is the digraph D by assigning signs 1 or −1 to each arc of D. The base of S is the minimum number k such that there is a pair walks which have the same initial and terminal point with length k, but different signs. In this paper we show that for n ≥ 5 the upper bound of the base of a primitive non-powerful signed tournament Sn, which is the signed digraph by assigning 1 or −1 to each arc of a primitive tournament Tn, is max{2n + 2, n + 11}. Moreover we show that it is extremal except when n = 5, 7.
منابع مشابه
The kth upper bases of primitive non-powerful signed digraphs
In this paper, we study the kth upper bases of primitive non-powerful signed digraphs. A bound on the kth upper bases of all primitive non-powerful signed digraphs is obtained, and the equality case of the bound is characterized. We also show that there exists “gap” in the kth upper base set of primitive non-powerful signed digraphs. AMS classification: 05C20, 05C50, 15A48
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Article history: Received 3 June 2010 Accepted 2 November 2010 Available online 26 November 2010 Submitted by R.A. Brualdi AMS classification: 05C50 15A09 15A48
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