http://researchonline.federation.edu.au/vital/access/manager/Index ${session.getAttribute("locale")} 5 http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:1775 Wed 07 Apr 2021 13:32:50 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:882 Wed 07 Apr 2021 13:31:52 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:871 Wed 07 Apr 2021 13:31:51 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:870 Wed 07 Apr 2021 13:31:51 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:845 Wed 07 Apr 2021 13:31:50 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:717 Wed 07 Apr 2021 13:31:41 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:656 Wed 07 Apr 2021 13:31:37 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:655 Wed 07 Apr 2021 13:31:36 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:654 Wed 07 Apr 2021 13:31:36 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:603 1 and k>1. Similarly, the Moore bound for an undirected graph of maximum degree d and diameter k is . Undirected Moore graphs only exist in a small number of cases. Mixed (or partially directed) Moore graphs generalize both undirected and directed Moore graphs. In this paper, we shall show that all known mixed Moore graphs of diameter k=2 are unique and that mixed Moore graphs of diameter k3 do not exist.]]> Wed 07 Apr 2021 13:31:33 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:522 = root(delta + 1) for g >= 7 odd. This result supports the conjecture of Fu, Huang and Rodger that all (delta; g)-cages are delta-connected. (c) 2005 Elsevier B.V. All rights reserved.]]> Wed 07 Apr 2021 13:31:27 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:521 Wed 07 Apr 2021 13:31:27 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:424 Wed 07 Apr 2021 13:31:20 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:332 Wed 07 Apr 2021 13:31:13 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:286 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.]]> Wed 07 Apr 2021 13:31:10 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:100 1, diameter k > 1 is a diregular digraph with the number of vertices one less than the Moore bound. If G is an almost Moore digraph, then for each vertex u ∈ V (G) there exists a vertex v ∈ V (G), called repeat of u and denoted by r (u) = v, such that there are two walks of length ≤ k from u to v. The smallest positive integer p such that the composition rp (u) = u is called the order of u. If the order of u is 1 then u is called a selfrepeat. It is known that if G is an almost Moore digraph of diameter k ≥ 3 then G contains exactly k selfrepeats or none. In this paper, we propose an exact formula for the number of all vertex orders in an almost Moore digraph G containing selfrepeats, based on the vertex orders of the out-neighbours of any selfrepeat vertex. © 2007 Elsevier B.V. All rights reserved.]]> Wed 07 Apr 2021 13:30:55 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:95 Wed 07 Apr 2021 13:30:55 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:93 Wed 07 Apr 2021 13:30:54 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:92 Wed 07 Apr 2021 13:30:54 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:64 Wed 07 Apr 2021 13:30:52 AEST ]]> http://researchonline.federation.edu.au/vital/access/manager/Repository/vital:62 Wed 07 Apr 2021 13:30:52 AEST ]]>