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On the exponent of a primitive, minimally strong digraph

โœ Scribed by Yang Shangjun; George P. Barker


Publisher
Elsevier Science
Year
1988
Tongue
English
Weight
960 KB
Volume
99
Category
Article
ISSN
0024-3795

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๐Ÿ“œ SIMILAR VOLUMES


On strong digraphs with a unique minimal
โœ Richard A. Brualdi; Rachel Manber ๐Ÿ“‚ Article ๐Ÿ“… 1988 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 659 KB

In this paper we determine the maximum number of &ges that a strong digraph can have if it has a unique minimally stroug subdigraph. We show that this number equais lrils = I)/2 + 1. Furthermore we show that there is, &to an isomorphism, a unique strong &graph which attains this maximum.

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## Abstract In this paper the conjecture on the __k__th upper multiexponent of primitive matrices proposed by R.A. Brualdi and Liu are completely proved.

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In this paper we present the upper and lower bounds of the longest directed cycle length for minimal strr,ng digraphs in terms of the numbers of vertices and arcs. These bounds are both sharp. In addition, we give analogous results for minimal 2-edge connected graphs.