EN
Digraph Groups Without Leaf Having An Arc Count One Greater Than Their Vertex
Abstract
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.
Keywords
References
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Details
Primary Language
English
Subjects
Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)
Journal Section
Research Article
Authors
Publication Date
June 30, 2025
Submission Date
March 12, 2025
Acceptance Date
June 11, 2025
Published in Issue
Year 2025 Volume: 46 Number: 2