2018/02/23 by Ankit Raj, Raj, Ankit, Shubh N. Singh +1
Engineering · Mathematics · #05C25 #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1802.08505
openalex publication_date 2018/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The power graph G(G) of a group G is a simple graph whose vertices are the elements of G and two distinct vertices are adjacent if one is a power of other. In this paper, we investigate the Laplacian spectrum of the power graph G(ℤpmn) of finite abelian p-group ℤpmn. In particular, we prove that the spectrum of group ℤpmn is contained in the Laplacian spectrum of graph G(ℤpmn). For a finite abelian group G whose power graph G(G) is planar, we also prove that the spectrum of group G is contained in the Laplacian spectrum of graph G(G).