Citation
Abstract
Gordon and McMahon defined a two-variable greedoid polynomial f(G; t, z) for any greedoid G. They studied greedoid polynomials for greedoids associated with rooted graphs and rooted digraphs. They proved that greedoid polynomials of rooted digraphs have the multiplicative direct sum property. In addition, these polynomials are divisible by 1 +Z under certain conditions. We compute the greedoid polynomials for all rooted digraphs up to order six. A polynomial is said to factorise if it has a non-constant factor of lower degree. We study the factorability of greedoid polynomials of rooted digraphs, particularly those that are not divisible by 1 + Z. We give some examples and an infinite family of rooted digraphs that are not direct sums but their greedoid polynomials factorise.
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Official URL or Download Paper: https://link.springer.com/article/10.1007/s00373-0...
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Additional Metadata
Item Type: | Article |
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Divisions: | Faculty of Science |
DOI Number: | https://doi.org/10.1007/s00373-021-02347-0 |
Publisher: | Springer |
Keywords: | Factorisation; Greedoid polynomial; Greedoid; Directed branching greedoid; Rooted digraph; Arborescence |
Depositing User: | Mr. Mohamad Syahrul Nizam Md Ishak |
Date Deposited: | 19 Aug 2024 02:07 |
Last Modified: | 19 Aug 2024 02:07 |
Altmetrics: | http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1007/s00373-021-02347-0 |
URI: | http://psasir.upm.edu.my/id/eprint/97264 |
Statistic Details: | View Download Statistic |
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