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Finding dense spanning trees (DST) in unweighted graphs is a variation of the well studied minimum spanning tree problem (MST). We utilize established mathematical properties of extremal structures with the minimum sum of distances between vertices to formulate some general conditions on the sum of vertex degrees. We analyze the performance of various combinations of these degree sum conditions in finding dense spanning subtrees and apply our approach to practical examples. After brieflydoi:10.1371/journal.pone.0184912 pmid:28926585 pmcid:PMC5605090 fatcat:a4cy5k6zkbexbilg3btqgtjwei