Abstract
Let G be a connected graph of order n. The eccentricity e(v) of a vertex v is the distance from v to a vertex farthest from v. The average eccentricity of G is the mean of all eccentricities in G. We give upper bounds on the average eccentricity of G in terms of order n, minimum degree δ, and girth g. In addition, we construct graphs to show that, if for given g and δ, there exists a Moore graph of minimum degree δ and girth g, then the bounds are asymptotically sharp. Moreover, we show that the bounds can be improved for a graph of large degree Δ.
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