Forbidden Subgraphs of Prime Order Element Graph

2024/12/27 by Manna, Tapa, Das, Angsuman, Bhattacharya, Baby · 1 citation
#05C17 #05C25 #05E16 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2412.19905

Abstract

In this paper, we study different forbidden subgraph characterizations of the prime-order element graph Γ(G) defined on a finite group G. Its set of vertices is the group G and two vertices x,y ∈ G are adjacent if the order of xy is prime. More specifically, we investigate the conditions when Γ(G) is perfect, cograph, chordal, claw-free, and interval graph.

Cited by

• Prime Order Element Graph of a Group -- II

Related

• Forbidden Subgraphs of co-prime Graphs of finite Groups
• Prime Order Element Graph of a Group -- II
• On power graphs of finite groups with forbidden induced subgraphs
• The co-prime order graph associated with a finite group
• The non-two-primes graph of a finite group