Characteristic polynomials of production matrices for geometric graphs

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/111649

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor	Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
dc.contributor.author	Huemer, Clemens
dc.contributor.author	Pilz, Alexander
dc.contributor.author	Seara Ojea, Carlos
dc.contributor.author	Silveira, Rodrigo Ignacio
dc.date	2017-08-01
dc.identifier.citation	Huemer, 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.
dc.identifier.citation	1571-0653
dc.identifier.citation	10.1016/j.endm.2017.07.017
dc.identifier.uri	http://hdl.handle.net/2117/111649
dc.language.iso	eng
dc.relation	http://www.sciencedirect.com/science/article/pii/S1571065317301828?via%3Dihub
dc.relation	This project has received funding from the European Union’s Horizon 89 2020 research and innovation programme under the Marie Sk lodowska- 90 Curie grant agreement No 734922. 91 C. H., C. S., and R. I. S. were partially supported by projects MINECO MTM2015- 92 63791-R and Gen. Cat. DGR2014SGR46. R. I. S. was also supported by MINECO 93 through the Ramon y Cajal program
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
dc.subject	Graph theory
dc.subject	Fibonacci number
dc.subject	geometric graph
dc.subject	production matrix
dc.subject	Riordan array
dc.subject	Grafs, Teoria de
dc.title	Characteristic polynomials of production matrices for geometric graphs
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/article
dc.description.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.

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