Compiling vocabularies of nonoverlapping codons with graph theory and SageMath

Vladimir R Rosenfeld

doi:10.1016/j.biosystems.2023.105033

Compiling vocabularies of nonoverlapping codons with graph theory and SageMath

Biosystems. 2023 Nov:233:105033. doi: 10.1016/j.biosystems.2023.105033. Epub 2023 Sep 16.

Author

Vladimir R Rosenfeld¹

Affiliation

¹ Department of Mathematics, Ariel University, Ariel 4070000, Israel. Electronic address: vladimir_rosenfeld@yahoo.com.

PMID: 37722480
DOI: 10.1016/j.biosystems.2023.105033

Abstract

We consider the compilation of complete (nonextensible) dictionaries of pairwise nonoverlapping codons containing the maximum possible number of such codons. This includes three subcases: (a) codons that do not allow overlapping by two letters, but allowing overlapping by one letter (e.g., ATC and CTG); (b) on the contrary, codons that do not allow only overlapping by one letter, but allow overlapping by two letters (e.g., ATC and TCG); (c) when there can be no overlap (as ATC and GTC). The last subcase is also an example of the nonoverlapping code that is used in coding theory and automata theory. Herein, we use graph theory and the SageMath computer algebra system as working tools.

Keywords: Independence polynomial; Independent set; SageMath; Vocabularies of nonoverlapping codons.