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Mixed Moore Cayley Graphs

Erskine, Grahame (2017). Mixed Moore Cayley Graphs. Journal of Interconnection Networks, 17(03n04), article no. 1741010.

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The degree-diameter problem seeks to find the largest possible number of vertices in a graph having given diameter and given maximum degree. There has been much recent interest in the problem for mixed graphs, where we allow both undirected edges and directed arcs in the graph. For a diameter 2 graph with maximum undirected degree r and directed out-degree z, a straightforward counting argument yields an upper bound M(z,r,2)=(z+r)2+z+1 for the order of the graph. Apart from the case r=1, the only three known examples of mixed graphs attaining this bound are Cayley graphs, and there are an infinite number of feasible pairs (r,z) where the existence of mixed Moore graphs with these parameters is unknown. We use a combination of elementary group-theoretical arguments and computational techniques to rule out the existence of further examples of mixed Cayley graphs attaining the Moore bound for all orders up to 485.

Item Type: Journal Item
ISSN: 0219-2659
Keywords: Degree-diameter problem; mixed graphs; Moore graphs
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 52715
Depositing User: Grahame Erskine
Date Deposited: 20 Dec 2017 14:49
Last Modified: 15 Sep 2018 19:25
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