Finding spanning trees under various restrictions has been an interesting question to researchers. A "dense" tree, from a graph theoretical point of view, has small total distances between vertices and large number of substructures. In this note, the "density" of a spanning tree is conveniently measured by the weight of a tree (defined as the sum of products of adjacent vertex degrees). By utilizing established conditions and relations between trees with the minimum total distance or maximum number of sub-trees, an edge-swap heuristic for generating "dense" spanning trees is presented. Computational results are presented for randomly generated graphs and specific examples from applications.
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Ozen, Mustafa; Wang, Hua; Wang, Kai; and Yalman, Demet
"An Edge-Swap Heuristic for Finding Dense Spanning Trees,"
Theory and Applications of Graphs: Vol. 3
, Article 1.
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol3/iss1/1