Vertex-weightings for distance moments and thorny graphs
Valence-weightings are considered for shortest-path distance moments, as well as related weightings for the so-called Wiener polynomial. In the case of trees the valence-weighted quantities are found to be expressible as a combination of unweighted quantities. Further the weighted quantities for a so-called thorny graph are considered and shown to be related to the weighted and unweighted quantities for the underlying parent graph.
primary 05c12 05c05 secondary 05c90