Digraph Groups Without Leaf Having An Arc Count One Greater Than Their Vertex
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| Názov: | Digraph Groups Without Leaf Having An Arc Count One Greater Than Their Vertex |
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| Autori: | Mehmet Sefa Cihan |
| Zdroj: | Volume: 46, Issue: 2410-423 Cumhuriyet Science Journal |
| Informácie o vydavateľovi: | Cumhuriyet University, 2025. |
| Rok vydania: | 2025 |
| Predmety: | Kombinatorik ve Ayrık Matematik (Fiziksel Kombinatorik Hariç), Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics), Digraph group, Pride group, Finite cyclic, Rank, Presentations |
| Popis: | This paper investigates a particular class of digraph groups that are defined by non-empty balanced presentations. Each relation is expressed in the form R(x,y), where x and y are distinct generators, and R(⋅,⋅) is based on a fixed cyclically reduced word R(a,b) involving both a and b. A directed graph is constructed for each such presentation, where vertices correspond to generators and edges represent the relations. In previous research, Cihan identified 35 families of digraphs that satisfy |V(Γ)|=|A(Γ)|-1, of which 11 of them do not contain leaves. This paper demonstrates that, with two exceptions, the rank of the associated groups is either 1 or 2. |
| Druh dokumentu: | Article |
| Popis súboru: | application/pdf |
| ISSN: | 2587-2680 |
| DOI: | 10.17776/csj.1656241 |
| Prístupová URL adresa: | https://dergipark.org.tr/tr/pub/csj/issue/93334/1656241 |
| Prístupové číslo: | edsair.doi.dedup.....9ef47c203022adbe07fa89c4b86750b5 |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | This paper investigates a particular class of digraph groups that are defined by non-empty balanced presentations. Each relation is expressed in the form R(x,y), where x and y are distinct generators, and R(⋅,⋅) is based on a fixed cyclically reduced word R(a,b) involving both a and b. A directed graph is constructed for each such presentation, where vertices correspond to generators and edges represent the relations. In previous research, Cihan identified 35 families of digraphs that satisfy |V(Γ)|=|A(Γ)|-1, of which 11 of them do not contain leaves. This paper demonstrates that, with two exceptions, the rank of the associated groups is either 1 or 2. |
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| ISSN: | 25872680 |
| DOI: | 10.17776/csj.1656241 |