Abstract
AbstractThe mean distance, μ(G), of a graph G is the arithmetic mean of the distances in G. Upper and lower bounds for the mean distance of a self‐complementary graph of given order are obtained and the extremal grpahs are determined. It is shown that if t ≥ 2 is rational, then there exist (1) graphs with arbitrarily low or high edge density, (2) bipartite graphs and (3) oriented graphs with mean distance equal to t, and also (4) trees and (5) tournaments with mean distance arbitrarily close to t. A number of open problems are mentioned.
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