Abstract
An almost Moore (d, k)-digraph is a regular digraph of degree \({d > 1}\), diameter \({k > 1}\) and order \({N(d, k) = d + d^{2} +\cdots + d^{k}}\). So far, their existence has only been showed for k = 2. Their nonexistence has been proved for k = 3, 4 and for d = 2, 3 when \({k \geq 3}\). In this paper, we prove that (4, k) and (5, k)-digraphs with self-repeats do not exist for infinitely many primes k.
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Research of the authors was supported in part by Grants MTM2013-46949-P (Spanish Ministerio de Ciencia e Innovación) and 2014SGR-1666 (Generalitat de Catalunya).
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Conde, J., Miller, M., Miret, J.M. et al. On the Nonexistence of Almost Moore Digraphs of Degree Four and Five. Math.Comput.Sci. 9, 145–149 (2015). https://doi.org/10.1007/s11786-015-0219-z
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DOI: https://doi.org/10.1007/s11786-015-0219-z