Kang, Andy N. C.Ault, David A.2013-06-192013-06-191974http://hdl.handle.net/10919/20275The notions of a balance node and the total path length with respect to a node u of a spanning tree are defined. We show that the total path length of a spanning tree with respect to u is minimal if and only if u is a balance node. An algorithm is also given to locate a balance node. A proof of the correctness of the algorithm is given and the complexity of the algorithm is analyzed.application/pdfenIn CopyrightTechnical reportCS74032-Rhttp://eprints.cs.vt.edu/archive/00000785/01/CS74032-R.pdf