Line Graph Characterization of Cyclic Subgroup Graph

2025/03/15 by Malviy, Siddharth, Kakkar, Vipul, Srivastava, Swapnil
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.12184

Abstract

The cyclic subgroup graph Γ(G) of a group G is the simple undirected graph with cyclic subgroups as a vertex set and two distinct vertices H₁ and H₂ are adjacent if and only if H₁ ≤ H₂ and there does not exist any cyclic subgroup K such that H₁ < K < H₂. In this paper, we classify all the finite groups G such that Γ(G) is the line graph of some graph.

Related

• Cyclic Subgroup Graph of a Group
• Finite groups whose commuting graphs are line graphs
• Line graph characterization of the order supergraph of a finite group
• Finite groups with regular subgroup graph
• Generalized power graph of groups