Branch duplication in trees

uniqueness of seeds and enumeration of seeds

Authors

  • Charles R. Johnson The College of William and Mary.
  • Jacob Lettie Duke University.
  • Sander Mack-Crane Case Western Reserve University.
  • Alicja Szabelska-Beręsewicz Poznan University of Life Sciences. https://orcid.org/0000-0002-1806-0891

DOI:

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

Keywords:

Branch duplication in trees, Enumeration of seeds, Rooted trees, Seeds, Uniqueness of seeds

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.

Author Biographies

Charles R. Johnson, The College of William and Mary.

Department of Mathematics,

Jacob Lettie, Duke University.

Department of Mathematics.

Sander Mack-Crane, Case Western Reserve University.

Department of Mathematics, Applied Mathematics and Statistics.

Alicja Szabelska-Beręsewicz, Poznan University of Life Sciences.

Dept. of Mathematical and Statistical Methods.

References

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.

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

A. Leal-Duarte and C. 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

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

Published

2020-04-29

How to Cite

[1]
C. R. Johnson, J. Lettie, S. Mack-Crane, and A. Szabelska-Beręsewicz, “Branch duplication in trees: uniqueness of seeds and enumeration of seeds”, Proyecciones (Antofagasta, On line), vol. 39, no. 2, pp. 451-465, Apr. 2020.

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