${session.getAttribute("locale")} 5 On mixed Moore graphs Wed 19 Dec 2018 14:40:33 AEDT ]]> On the degrees of a strongly vertex-magic graph Wed 09 Jan 2019 14:14:53 AEDT ]]> A sum labelling for the generalised friendship graph Wed 09 Jan 2019 11:10:58 AEDT ]]> Enumerations of vertex orders of almost Moore digraphs with selfrepeats 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.]]> Tue 08 Jan 2019 16:33:17 AEDT ]]> HSAGA and its application for the construction of near-Moore digraphs Tue 08 Jan 2019 14:11:38 AEDT ]]> Complete characterization of almost moore digraphs of degree three Thu 21 Feb 2019 16:54:37 AEDT ]]> All (k;g)-cages are k-edge-connected Mon 17 Dec 2018 15:29:40 AEDT ]]> Characterization of eccentric digraphs Mon 16 Jan 2017 20:52:02 AEDT ]]> A lower bound on the order of regular graphs with given girth pair Mon 16 Jan 2017 11:21:22 AEDT ]]> Graphs of order two less than the Moore bound 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.]]> Mon 10 Dec 2018 09:18:37 AEDT ]]> On the connectivity of (k, g)-cages of even girth Mon 10 Dec 2018 09:16:33 AEDT ]]> Consecutive magic graphs Fri 11 Jan 2019 10:10:52 AEDT ]]>