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Degree diameter problem

In graph theory, the degree–diameter problem asks for the maximum possible number n d , k {\displaystyle n_{d,k}} of vertices in a finite simple undirected graph of maximum degree at most d {\displaystyle d} and diameter at most k {\displaystyle k} . A breadth-first search gives a general upper bound known as the Moore bound.

Bounds and constructions, Asymptotic behaviour & Relation to the degree–girth problem