Digraph Groups Without Leaf Having An Arc Count One Greater Than Their Vertex

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 gr...

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Bibliographic Details
Published in:Cumhuriyet Science Journal Vol. 46; no. 2; pp. 410 - 423
Main Author: Cihan, Mehmet Sefa
Format: Journal Article
Language:English
Published: Sivas Cumhuriyet Üniversitesi 30.06.2025
Subjects:
digraph group
finite cyclic
pride group
rank
ISSN:2587-2680
Online Access:Get full text
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Summary: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.
ISSN:2587-2680
DOI:10.17776/csj.1656241