Digraphs of degree and order close to the Moore bound
نویسندگان
چکیده
It is known that Moore digraphs of degree d and diameter k do not ex ist see or Furthermore for degree it is shown that for k there are no digraphs of order close to i e one less than Moore bound In this paper we shall consider digraphs of diameter k degree and number of vertices one less than Moore bound We give a necessary condition for the existence of such digraphs and using this condition we deduce that such digraphs do not exist for in nitely many values of the diameter
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Regular digraphs of diameter 2 and maximum order
It is known that Moore digraphs of degree d > 1 and diameter k > 1 do not exist (see [16] or [4]). For degree 2, it has been shown that for diameter k ~ 3 there are no digraphs of order 'close' to, i.e., one less than, the Moore bound (14). For diameter 2, it is known that digraphs close to Moore bound exist for any degree because the line digraphs of complete digraphs are an example of such di...
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