https://nova.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:10001 Sat 24 Mar 2018 08:12:22 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:9999 1 and diameter k = 2m are obtained. In the case δ = 1, which corresponds to almost Moore digraphs, a necessary condition in terms of the permutation cycle structure is derived. Additionally, we present some constructions of dense multipartite digraphs of diameter two that are vertex-transitive.]]> Sat 24 Mar 2018 08:12:15 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:20998 1, diameter at most k>1 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 k>4 and d>3, under the assumption of a conjecture related to the factorization of the polynomials Φ_n(1+x+⋯+x^k), where Φn(x) denotes the nnth cyclotomic polynomial and 1 Sat 24 Mar 2018 07:50:39 AEDT ]]>