Factorization graphs of finite groups

2019/11/28 by Mohammad Farrokhi Derakhshandeh Ghouchan, Ghouchan, Mohammad Farrokhi Derakhshandeh, Ali Azimi +1
Computer Science · Engineering · Mathematics · #05C40 #05C75 (Secondary) #20D40 (Primary) 05C25 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.CO #math.GR #msc:05C25 #msc:05C40 #msc:05C75 #msc:20D40

paper · pdf · doi:10.48550/arxiv.1911.12594

13 pages

arxiv created 2019/11/28 · openalex publication_date 2019/11/28 · arxiv updated 2019/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the factorization graph of a finite group and study its connectedness and forbidden structures. We characterize all finite groups with connected factorization graphs and classify those with connected bipartite factorization graphs. Also, we obtain a classification of all groups with claw-free, K_1,4-free, and square-free factorization graphs, excluding the non-solvable groups in the latter case.

Related

• On power graphs of finite groups with forbidden induced subgraphs
• On finite groups whose power graph is claw-free
• Some properties of various graphs associated with finite groups
• 1-Factorizations of Cayley graphs
• Factorizations of finite groups