Abstract
A Moore graph of type ( d, k) is a regular graph of degree d, diameter k, and girth 2 k + 1. By counting the cycles of length 2 k + 1 and 2 k + 2 of a Moore graph, it is shown that there are no Moore graphs of type ( d, k) for d = 3, 4, 5, 6, 8 and 3 < k ≤ 300 except possibly for type (5, 7). It is shown that there are no Moore graphs of type (3, k) when 3 ≤ k < ∞ and 2 k + 1 is prime.
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