2023/12/14 by Sandeep Dalal, Dalal, Sandeep, Sanjay Mukherjee +3
Engineering · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2312.08930
openalex publication_date 2023/12/14 · openalex created_date 2023/12/16 · openalex updated_date 2026/07/28
Let Γ be a simple finite graph with vertex set V(Γ) and edge set E(Γ). Let R be an equivalence relation on V(Γ). The R-super Γ graph ΓR is a simple graph with vertex set V(Γ) and two distinct vertices are adjacent if either they are in the same R-equivalence class or there are elements in their respective R-equivalence classes that are adjacent in the original graph Γ. We first show that ΓR is a generalized join of some complete graphs and using this we obtain the adjacency and Laplacian spectrum of conjugacy and order super commuting graphs of dihedral group D2n (n≥ 3), generalized quaternion group Q4m (m≥ 2) and the nonabelian group \mathbb Zp \rtimes \mathbb Zq of order pq, where p and q are distinct primes with q|p-1.