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arXiv · 0806.1438

On Mean Distance and Girth

Siham Bekkai·Mekkia Kouider
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Abstract

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.

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Siham Bekkai, Mekkia Kouider. 2013-01-04. On Mean Distance and Girth. https://arxiv.org/abs/0806.1438

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