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- W2078598049 abstract "We obtain exact bounds for the girth and the diameter of a vertex-transitive digraph. As an application of the above results we obtain the following. Let G be a group and S be a generating subset such that 1 ∉ S, card((G) = n and card(S) = s. Then the unity of G is the product of a sequence of elements of S with length not exceeding ⌈n/s⌉. If x is an arbitrary element of G then x is the product of a sequence of elements of G with length not exceeding (2n−2s−5)/s. The bounds obtained in the paper are exact. We solve also the problem in the cases S = S−1 and S∩S−1=∅." @default.
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- W2078598049 date "1981-12-01" @default.
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- W2078598049 title "An Application of Connectivity Theory in Graphs to Factorizations of Elements in Groups" @default.
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- W2078598049 doi "https://doi.org/10.1016/s0195-6698(81)80042-x" @default.
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