Super commuting graphs of finite groups and their Zagreb indices

2024/07/16 by Shrabani Das, Rajat Kanti Nath, Das, Shrabani +1
Chemistry · Mathematics · #20E45 #FOS: Mathematics #Graph theory and applications #Group Theory (math.GR) #History and advancements in chemistry #Primary: 20D60 #Secondary: 05C25 #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.2407.11297

openalex publication_date 2024/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let B be an equivalence relation defined on a finite group G. The B super commuting graph on G is a graph whose vertex set is G and two distinct vertices g and h are adjacent if either [g] = [h] or there exist g' ∈ [g] and h' ∈ [h] such that g' commutes with h', where [g] is the B-equivalence class of g ∈ G. Considering B as the equality, conjugacy and same order relations on G, in this article, we discuss the graph structures of equality/conjugacy/order super commuting graphs of certain well-known families of non-abelian groups viz. dihedral groups, dicyclic groups, semidihedral groups, quasidihedral groups, the groups U_6n, V_8n, M_2mn etc. Further, we compute the Zagreb indices of these graphs and show that they satisfy Hansen-Vukičević conjecture.

Related

• Commuting Conjugacy Class Graphs of Finite Groups and the Hansen-Vukičević Conjecture
• Spectrum of conjugacy and order super commuting graphs of some finite groups
• Super graphs on groups, I
• Super graphs on groups, II
• Zagreb indices of commuting and non-commuting graphs of finite groups and Hansen-Vukičević conjecture