Abstract
A Moore ( d, k)-graph is a regular graph of degree d with diameter k and girth 2 k + 1. It is proved that every edge of a Moore ( d, k)-graph is contained in the same number r m cycles of length m, where m ⩽ 4 k + 1. A recurrence relation for r m is given. Further, some corollaries, as for the impossibility of certain Moore graphs, are shown, e.g., if 3 ⩽ d ⩽ 100 and 3 ⩽ k ⩽ 100, then there is no Moore ( d, k)-graph.
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