Associative triples and homomorphisms between travel groupoids on finite geodetic graphs

We characterize trees, block graphs, and odd cycles in the class of geodetic graphs using the algebraic structure induced by the travel operation.We then obtain a criterion for associative triples in travel groupoids on geodetic graphs.Finally, we extend the characterization of homomorphisms between travel groupoids from trees to general geodetic graphs.

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Publication Details

Journal
Discrete Mathematics Letters
Published
2025-12-31
DOI
https://doi.org/10.47443/dml.2025.193
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
article
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article

Associative triples and homomorphisms between travel groupoids on finite geodetic graphs

Sergiy Kozerenko, Yur-Liubomysl Dekhtiar
Discrete Mathematics Letters
Homotopy and Cohomology in Algebraic Topology
article

Associative triples and homomorphisms between travel groupoids on finite geodetic graphs

Sergiy Kozerenko, Yur-Liubomysl Dekhtiar
article en

Abstract

We characterize trees, block graphs, and odd cycles in the class of geodetic graphs using the algebraic structure induced by the travel operation.We then obtain a criterion for associative triples in travel groupoids on geodetic graphs.Finally, we extend the characterization of homomorphisms between travel groupoids from trees to general geodetic graphs.

Discrete Mathematics LettersVol. 16
Reduced inequalities
Openalex Percentile: Top 20%
Homotopy and Cohomology in Algebraic Topology
DOIOpen Access PDFOpenAlex
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Associative triples and homomorphisms between travel groupoids on finite geodetic graphs — Sergiy Kozerenko, Yur-Liubomysl Dekhtiar · Discrete Mathematics Letters (2025) | TGRS Research Map | TGRS