The Bases of Primitive Non-powerful Complete Signed Graphs
نویسندگان
چکیده
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.
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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