On the existence of (d,k)-digraphs
Discrete Mathematics
Almost Moore digraphs are diregular
Discrete Mathematics
Enumeration of almost Moore digraphs of diameter two
Discrete Mathematics - Special issue on the 17th british combinatorial conference selected papers
Line digraph iterations and the (d,k) problem for directed graphs
ISCA '83 Proceedings of the 10th annual international symposium on Computer architecture
Complete characterization of almost Moore digraphs of degree three
Journal of Graph Theory
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Digraphs of maximum out-degree at most d1, diameter at most k1 and order N(d,k)=d+...+d^k are called almost Moore or (d,k)-digraphs. So far, the problem of their existence has been solved only when d=2,3 or k=2,3,4. In this paper we derive the nonexistence of (d,k)-digraphs, with k4 and d3, under the assumption of a conjecture related to the factorization of the polynomials @F"n(1+x+...+x^k), where @F"n(x) denotes the nth cyclotomic polynomial and 1