Distance matrix of enhanced power graphs of finite groups

2023/04/09 by Arora, Anita, Dey, Hiranya Kishore, Goel, Shivani
#05C25 #05C50 #20K01 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.04288

Abstract

The enhanced power graph of a group G is the graph G_E(G) with vertex set G and edge set \(u,v): u, v ∈ ⟨ w ⟩,~for some~ w ∈ G\. In this paper, we compute the spectrum of the distance matrix of the enhanced power graph of non-abelian groups of order pq, dihedral groups, dicyclic groups, elementary abelian groups El(pⁿ) and the non-cyclic abelian groups El(pⁿ)\timesEl(q^m) and El(pⁿ)× ℤ_m, where p and q are distinct primes. For the non-cyclic abelian group El(pⁿ)× El(q^m), we also compute the spectrum of the adjacency matrix of its enhanced power graph and the spectrum of the adjacency and the distance matrix of its power graph.

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