Primitive non-powerful symmetric loop-free signed digraphs with given base and minimum number of arcs |
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Authors: | Lihua You Yuhan Wu |
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Affiliation: | School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China |
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Abstract: | In [B.M. Kim, B.C. Song, W. Hwang, Primitive graphs with given exponents and minimum number of edges, Linear Algebra Appl. 420 (2007) 648-662], the minimum number of edges of a simple graph on n vertices with exponent k was determined. In this paper, we completely determine the minimum number, H(n,k), of arcs of primitive non-powerful symmetric loop-free signed digraphs on n vertices with base k, characterize the underlying digraphs which have H(n,k) arcs when k is 2, nearly characterize the case when k is 3 and propose an open problem. |
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Keywords: | 05C50 15A09 15A48 |
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