We bound the mean distance in a connected graph which is not a tree in function of its order $n$ and its girth $g$. On one hand, we show that mean distance is at most $\frac{ n+1}{ 3}-\frac{ g(g^2-4)}{ 12n(n-1)}$ if $g$ is even and at most $\frac{ n+1}{ 3}-\frac{ g(g^2-1)}{ 12n(n-1)}$ if $g$ is odd. On the other hand, we prove that mean distance is at least $\frac{ ng}{ 4(n-1)}$ unless $G$ is an odd cycle.
Categories: cs.DM