Production matrices for geometric graphs

Clemens Huemer, Carlos Seara, Rodrigo I. Silveira, Alexander Pilz

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We present production matrices for non-crossing geometric graphs on point sets in convex position, which allow us to derive formulas for the numbers of such graphs. Several known identities for Catalan numbers, Ballot numbers, and Fibonacci numbers arise in a natural way, and also new formulas are obtained, such as a formula for the number of non-crossing geometric graphs with root vertex of given degree. The characteristic polynomials of some of these production matrices are also presented. The proofs make use of generating trees and Riordan arrays.

Original languageEnglish
Pages (from-to)301-306
Number of pages6
JournalElectronic Notes in Discrete Mathematics
Volume54
DOIs
Publication statusPublished - 1 Oct 2016
Externally publishedYes

Fingerprint

Geometric Graphs
Riordan Arrays
Generating Trees
Catalan number
Lame number
Polynomials
Characteristic polynomial
Point Sets
Roots
Graph in graph theory
Vertex of a graph

Keywords

  • Catalan number
  • geometric graph
  • production matrix
  • Riordan array

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Production matrices for geometric graphs. / Huemer, Clemens; Seara, Carlos; Silveira, Rodrigo I.; Pilz, Alexander.

In: Electronic Notes in Discrete Mathematics, Vol. 54, 01.10.2016, p. 301-306.

Research output: Contribution to journalArticleResearchpeer-review

Huemer, Clemens ; Seara, Carlos ; Silveira, Rodrigo I. ; Pilz, Alexander. / Production matrices for geometric graphs. In: Electronic Notes in Discrete Mathematics. 2016 ; Vol. 54. pp. 301-306.
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