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- W2132290920 abstract "A digraph D is primitive if, for some positive integer r, there is a u → v walk of length r for every pair u , v of vertices of D. The minimum such r is called the exponent of D, denoted exp( D ). We prove that if a primitive digraph D of order n is an Abelian Cayley digraph with degree k ⩾4, then exp (D)⩽ max 5, n ⌈k/2⌉ −1 . If we assume only that the primitive digraph D is vertex-transitive, then we are able to prove that exp (D)⩽ n k n k +1 . Finally, we make a conjecture on the exponents of all regular primitive digraphs." @default.
- W2132290920 created "2016-06-24" @default.
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- W2132290920 date "2000-02-01" @default.
- W2132290920 modified "2023-10-18" @default.
- W2132290920 title "Exponents of vertex-transitive digraphs" @default.
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- W2132290920 doi "https://doi.org/10.1016/s0012-365x(99)00291-5" @default.
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