Abstract
The diameters of graphs and their spanning trees have been extensively studied and used in a wide variety of applications. Another important invariant of a spanning tree is its distance sum—that is, the sum of the distances between each pair of nodes in the tree. First, several results on the possible values for diameters of spanning trees are reviewed. Then it is shown that although the corresponding properties do not hold for distance sums of spanning trees, some weaker results of a similar type are true.
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