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2015•Korean Journal of MathematicsOpen access

BASE OF THE NON-POWERFUL SIGNED TOURNAMENT

Byeong Moon Kim, Byung Chul Song

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Abstract

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 $n{\geq}5$ 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 $T_n$ , is max{2n + 2, n+11}. Moreover we show that it is extremal except when n = 5, 7.

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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 $n{\geq}5$ 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 $T_n$ , is max{2n + 2, n+11}. Moreover we show that it is extremal except when n = 5, 7.

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Available abstract

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 $n{\geq}5$ 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 $T_n$ , is max{2n + 2, n+11}. Moreover we show that it is extremal except when n = 5, 7.

Key concepts: Tournament, Digraph, Mathematics, Combinatorics, Base (topology), Arc (geometry), Upper and lower bounds, Point (geometry)

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