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Networks and Spanning Trees: The Juxtaposition of Prüfer and Boruvka

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Title: Networks and Spanning Trees: The Juxtaposition of Prüfer and Boruvka
Language: English
Authors: Lodder, Jerry
Source: PRIMUS. 2014 24(8):737-752.
Availability: Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals
Peer Reviewed: Y
Page Count: 16
Publication Date: 2014
Document Type: Journal Articles
Reports - Descriptive
Education Level: Higher Education
Postsecondary Education
Descriptors: College Mathematics, Mathematics Instruction, Computer Science Education, Graphs, Primary Sources, History, Mathematics, Undergraduate Students, Student Attitudes, Instructional Effectiveness
DOI: 10.1080/10511970.2014.896835
ISSN: 1051-1970
Abstract: 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.
Abstractor: As Provided
Number of References: 21
Entry Date: 2014
Accession Number: EJ1033369
Database: ERIC
FullText Text:
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  Data: 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.
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