4 - Moore Graphs
نویسنده
چکیده
Let C2k denote the cycle of length 2k and Cg = {C3, C4, . . . , Cg}. The girth of a graph G containing a cycle is the length of a shortest cycle in G, so a graph has girth at least g + 1 if it is Cg-free. The distance between vertices u and v in a graph G, denoted dG(u, v) is the minimum length of a uv-path in G. Then dG(·, ·) is a metric on V (G). The diameter of a connected graph G is max{dG(u, v) : u, v ∈ V (G)}.
منابع مشابه
Non-existence of bipartite graphs of diameter at least 4 and defect 2
The Moore bipartite bound represents an upper bound on the order of a bipartite graph of maximum degree ∆ and diameterD. Bipartite graphs of maximum degree ∆, diameterD and order equal to the Moore bipartite bound are called Moore bipartite graphs. Such bipartite graphs exist only if D = 2, 3, 4 and 6, and for D = 3, 4, 6, they have been constructed only for those values of ∆ such that ∆− 1 is ...
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تاریخ انتشار 2015