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 |
| 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. |
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| ISSN: | 1051-1970 |
| DOI: | 10.1080/10511970.2014.896835 |
