Primary Historical Sources in the Classroom

Graph Theory and Spanning Trees
  • Jerry Lodder
Part of the ICME-13 Monographs book series (ICME13Mo)


I study student response to learning from a specific historical curricular module and compare this to advantages of learning from historical sources cited in education literature. The curricular module is “Networks and Spanning Trees,” based on the original works of Arthur Cayley, Heinz Prüfer and Otakar Borůvka. Cayley identifies a compelling pattern in the enumeration of (labeled) trees, although his counting argument is incomplete. Prüfer provides an alternate proof of “Cayley’s formula” by counting all railway networks connecting n towns that contain the least number of segments. Borůvka develops one of the first algorithms for finding a minimal spanning tree by considering how best to connect n towns to an electrical network.


Historical sources Graph theory Trees Minimal spanning trees 



The author would like to thank the United States National Science Foundation under grants DUE 0717752 and DUE 1523747 for supporting this project. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA

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