In graph theory, the degree diameter problem is the problem of finding the largest possible graph G (in terms of the size of its vertex set V) of diameter k such that the largest degree of any of the vertices in G is at most d. The size of G is bounded above by the Moore bound; for 1 < k and 2 < d only the Petersen graph, the Hoffman-Singleton graph, and maybe a graph of diameter k = 2 and degree d = 57 attain the Moore bound. In general the largest degree-diameter graphs are much smaller in size than the Moore bound.
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