On groups with chordal power graph, including a classification in the case of finite simple groups

DOI10.1007/s10801-023-01262-2zbMath1530.05079arXiv2209.00317OpenAlexW4387341470MaRDI QIDQ6185342

Eda Kaja, Jendrik Brachter

Publication date: 8 January 2024

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.00317

zbMATH Keywords

direct productschordal graphsimple groupspower graphmaximal cycles in power graphs

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Paths and cycles (05C38) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Finite simple groups and their classification (20D05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The power graph of a finite group
• Cayley graphs as classifiers for data mining: the influence of asymmetries
• Characterizations and algorithmic applications of chordal graph embeddings
• Directed graphs and combinatorial properties of semigroups
• The strong metric dimension of the power graph of a finite group
• Quotients of the Hermitian curve from subgroups of \(\text{PGU}(3,q)\) without fixed points or triangles
• Forbidden subgraphs of power graphs
• On the soluble graph of a finite group
• The power graph of a torsion-free group of nilpotency class 2
• On the connectivity of the non-generating graph
• The non-commuting, non-generating graph of a nilpotent group
• On finite groups whose power graph is a cograph
• Undirected power graphs of semigroups
• On the structure of the power graph and the enhanced power graph of a group
• The diameter of the commuting graph of a finite group with trivial centre.
• On power graphs of finite groups with forbidden induced subgraphs
• A decomposition theorem for partially ordered sets
• Power graphs and semigroups of matrices
• On enhanced power graphs of finite groups
• A NEW TYPE OF SIMPLE GROUPS OF FINITE ORDER
• The Finite Simple Groups
• Perfect Elimination and Chordal Bipartite Graphs
• Graph Classes: A Survey
• On connectedness of power graphs of finite groups
• Primary cyclotomic units and a proof of Catalans conjecture
• Recent developments on the power graph of finite groups – a survey
• EXTENDING RESULTS OF MORGAN AND PARKER ABOUT COMMUTING GRAPHS
• A survey on enhanced power graphs of finite groups
• Graphs defined on groups
• Power graphs: A survey
• On Ree's Series of Simple Groups
• Endliche Gruppen I
• Algorithms for Minimum Coloring, Maximum Clique, Minimum Covering by Cliques, and Maximum Independent Set of a Chordal Graph
• Classification of non-solvable groups whose power graph is a cograph