2025/08/20 by Zekhaya B. Shozi, Shozi, Zekhaya B., Teresa L. Tacbobo +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2508.14865
openalex publication_date 2025/08/20 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
In this paper, we continue the study of the generator graph of a group. In 2023, Tacbobo [9] defined the generator graph of a nontrivial group to be the graph whose vertices are the elements of the group, with two vertices being adjacent if at least one of them is a generator of the group. Building on the properties established in [9], we prove that the diameter of the generator graph of a cyclic group is at most 2. Furthermore, we present explicit formulas for some topological indices of the generator graph of a cyclic group with n ≥ 2 elements and whose set of generators is S, expressed in terms of n and |S|. Lastly, we determine the metric dimension of the generator graph of a nontrivial cyclic group as a function of its order n.