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Characteristic polynomials of production matrices for geometric graphs

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10.1016/j.endm.2017.07.017
 
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hdl:2117/111649

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Huemer, ClemensMés informacióMés informacióMés informació
Pilz, Alexander
Seara Ojea, CarlosMés informacióMés informacióMés informació
Silveira, Rodrigo IgnacioMés informacióMés informacióMés informació
Document typeArticle
Defense date2017-08-01
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
An n×n production matrix for a class of geometric graphs has the property that the numbers of these geometric graphs on up to n vertices can be read off from the powers of the matrix. Recently, we obtained such production matrices for non-crossing geometric graphs on point sets in convex position [Huemer, C., A. Pilz, C. Seara, and R.I. Silveira, Production matrices for geometric graphs, Electronic Notes in Discrete Mathematics 54 (2016) 301–306]. In this note, we determine the characteristic polynomials of these matrices. Then, the Cayley-Hamilton theorem implies relations among the numbers of geometric graphs with different numbers of vertices. Further, relations between characteristic polynomials of production matrices for geometric graphs and Fibonacci numbers are revealed.
CitationHuemer, C., Pilz, A., Seara, C., Silveira, R.I. Characteristic polynomials of production matrices for geometric graphs. "Electronic notes in discrete mathematics", 1 Agost 2017, vol. 61, p. 1-7. 
URIhttp://hdl.handle.net/2117/111649
DOI10.1016/j.endm.2017.07.017
ISSN1571-0653
Publisher versionhttp://www.sciencedirect.com/science/article/pii/S1571065317301828?via%3Dihub
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