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On Mean Distance and Girth
, 2008
"... 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 n+1 3 − g(g2 −4) 12n(n−1) if g is even and at most n+1 3 − g(g2 −1) 12n(n−1) if g is odd. On the other hand, we prove that mean distance ..."
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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 n+1 3 − g(g2 −4) 12n(n−1) if g is even and at most n+1 3 − g(g2 −1) 12n(n−1) if g is odd. On the other hand, we prove that mean distance is at least unless G is an odd cycle.