Networks and Spanning Trees: the Juxtaposition of Prüfer and Boruvka

• Autores: Jerry Lodder
• Localización: Primus: problems, resources, and issues in mathematics undergraduate studies, ISSN 1051-1970, Vol. 24, Nº. 8, 2014, págs. 737-752
• Idioma: inglés
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• Resumen

  • This paper outlines a method for teaching topics in undergraduate mathematics or computer science via historical curricular modules. The contents of one module, �Networks and Spanning Trees,� are discussed from the original work of Arthur Cayley, Heinz Prüfer, and Otakar Boruvka that motivates the enumeration and application of trees in graph theory. Cayley correctly identifies a pattern for the number of (labeled) trees on n fixed vertices. Prüfer�s paper provides a rigorous verification of this pattern, whereas Boruvka�s paper offers one of the first algorithms for finding a minimal spanning tree over the domain of labeled trees. These latter two papers in juxtaposition offer a pleasing confluence of concepts and applications, written verbally before the modern terminology of graph theory had been formulated.