Abstract
AbstractLet G be a connected graph of order n and independence number α. We prove that G has a spanning tree with average distance at most , if , and at most , if . As a corollary, we obtain, for n sufficiently large, an asymptotically sharp upper bound on the average distance of G in terms of its independence number. This bound, apart from confirming and improving on a conjecture of Graffiti [8], is a strengthening of a theorem of Chung [1], and that of Fajtlowicz and Waller [8], on average distance and independence number of a graph.
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