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ERIC Number: EJ1007726
Record Type: Journal
Publication Date: 2013-Jan
Pages: 5
Abstractor: As Provided
Reference Count: 0
ISBN: N/A
ISSN: ISSN-0746-8342
The Combinatorial Trace Method in Action
Krebs, Mike; Martinez, Natalie C.
College Mathematics Journal, v44 n1 p32-36 Jan 2013
On any finite graph, the number of closed walks of length k is equal to the sum of the kth powers of the eigenvalues of any adjacency matrix. This simple observation is the basis for the combinatorial trace method, wherein we attempt to count (or bound) the number of closed walks of a given length so as to obtain information about the graph's eigenvalues, and vice versa. We give a brief overview and present some simple but interesting examples. The method is also the source of interesting, accessible undergraduate projects.
Mathematical Association of America. 1529 Eighteenth Street NW, Washington, DC 20036. Tel: 800-741-9415; Tel: 202-387-5200; Fax: 202-387-1208; e-mail: maahq@maa.org; Web site: http://www.maa.org/pubs/cmj.html
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A