Branch duplication in trees: uniqueness of sedes and enumeration of sedes

Johnson, Charles R.; Lettie, Jacob; Mack-Crane, Sander; Szabelska-Beręsewicz, Alicja; Johnson, Charles R.; Lettie, Jacob; Mack-Crane, Sander; Szabelska-Beręsewicz, Alicja

doi:10.22199/issn.0717-6279-2020-02-0028

Servicios Personalizados

Revista

Articulo

Traducción automática

Indicadores

Citado por SciELO
Accesos

Links relacionados

Citado por Google
Similares en SciELO
Similares en Google

Otros
Otros

Permalink

Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.39 no.2 Antofagasta abr. 2020

http://dx.doi.org/10.22199/issn.0717-6279-2020-02-0028

Artículos

Branch duplication in trees: uniqueness of sedes and enumeration of sedes

Charles R. Johnson¹

Jacob Lettie²

Sander Mack-Crane³

Alicja Szabelska-Beręsewicz⁴
http://orcid.org/0000-0002-1806-0891

^¹The College of William and Mary, Dept. of Mathematics, Williamsburg, VA, U.S.A.: e-mail: crjohn@wm.edu

^²Duke University, Dept.of Mathematics, Durham, NC, U.S.A. e-mail: jrl47@duke.edu

^³Case Western Reserve University, Dept. of Mathematics, Applied Mathematics and Statistics, Cleveland, OH, U.S.A. e-mail: mack-crane@case.edu

^⁴Poznan University of Life Sciences, Dept. of Mathematical and Statistical Methods, Poznan, Poland. e-mail: aszabelska@gmail.com

Abstract

By the process of branch duplication, any tree may be generated from a type of tree called a seed. We describe the correspondence between trees and seeds by showing that each tree grows from a unique seed and giving an algorithm to produce this seed. Using results about the structure of seeds, we enumerate the seeds of a given diameter.

Keywords: Branch duplication in tres; Enumeration of sedes; Rooted tres; Seeds; Uniqueness of seeds

Texto completo disponible sólo en PDF

Full text available only in PDF format.

Acknowledgements

This work was supported by NSF grant DMS 075 1964.

References

[1] C. R. Johnson and C. M. Saiago, “Branch duplication for the construction of multiple eigenvalues in an Hermitian matrix whose graph is a tree”,Linear and multilinear algebra, vol. 56, no. 4, pp. 357-380, 2008, doi: 10.1080/03081080600597668. [ Links ]

[2] C. R. Johnson andC. M. Saiago , “Diameter minimal trees”, Linear and multilinear algebra, vol. 64, no. 3, pp. 557-571, 2015, doi: 10.1080/03081087.2015.1057097. [ Links ]

[3] A. Leal-Duarte andC. R. Johnson , “On the minimum number of distinct eigenvalues for a symmetric matrix whose graph is a given tree”,Mathematical Inequalities & Applications, vol. 5, no. 2, pp. 175-180, 2002, doi: 10.7153/mia-05-19. [ Links ]

[4] The R Fundation, “The R Project for Statistical Computing”, R-project, 2016. [Online]. Available: https://www.r-project.org/. [ Links ]

Received: June 30, 2019; Accepted: November 30, 2019

Article copyright: © 2020 Charles R. Johnson, Jacob Lettie, Sander Mack-Crane and Alicja Szabelska-Beręsewicz. This is an open access article distributed under the terms of the Creative Commons Licence, which permits unrestricted use and distribution provided the original author and source are credited.

This is an open-access article distributed under the terms of the Creative Commons Attribution License