Primitive non-powerful symmetric loop-free signed digraphs with given base and minimum number of arcs

✍ Scribed by Lihua You; Yuhan Wu

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 272 KB
• Volume: 434
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2010.11.003

✦ Synopsis

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.