A study of enhanced power graphs of finite groups

DOI10.1142/S0219498820500620zbMath1441.05111arXiv1810.07627OpenAlexW2920263613WikidataQ114614705 ScholiaQ114614705MaRDI QIDQ5113133

Rozália Sz. Madarász, Samir Zahirović, Ivica Bosnjak

Publication date: 2 June 2020

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.07627

zbMATH Keywords

graphautomorphismisomorphismperfect graphgroupenhanced power graph

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items

On the connected power graphs of semigroups of homogeneous elements of graded rings ⋮ Criterion of unrecognizability of a finite group by its Gruenberg-Kegel graph ⋮ On the connectivity of enhanced power graphs of finite groups ⋮ A survey on enhanced power graphs of finite groups ⋮ The rainbow connection number of the enhanced power graph of a finite group ⋮ Finite groups satisfying the independence property ⋮ Certain properties of the enhanced power graph associated with a finite group ⋮ Unnamed Item ⋮ Enhanced power graphs of groups are weakly perfect ⋮ Graphs defined on groups ⋮ On the proper enhanced power graphs of finite nilpotent groups ⋮ On the enhanced power graph of a finite group ⋮ On enhanced power graphs of certain groups

Cites Work

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• The structure and metric dimension of the power graph of a finite group
• The power graph of a finite group
• Minimal paths in the commuting graphs of semigroups
• Anisotropic groups of type \(A_n\) and the commuting graph of finite simple groups.
• On groups of even order
• The strong perfect graph theorem
• Cayley graphs as classifiers for data mining: the influence of asymmetries
• On finite homomorphic images of the multiplicative group of a division algebra
• Directed graphs and combinatorial properties of semigroups
• Coloring the power graph of a semigroup
• There is no upper bound for the diameter of the commuting graph of a finite group
• The commuting graph of the symmetric inverse semigroup
• 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.
• Finite groups generated by 3-transpositions. I
• The power graph of a torsion-free group
• Power graphs and semigroups of matrices
• On the power graph of a finite group
• Certain properties of the power graph associated with a finite group
• The power graph of a finite group, II
• On enhanced power graphs of finite groups
• On bounding the diameter of the commuting graph of a group
• ON THE COMMUTING GRAPH ASSOCIATED WITH THE SYMMETRIC AND ALTERNATING GROUPS
• On connectedness of power graphs of finite groups
• The diameter of power graphs of symmetric groups
• Power graphs: A survey
• On the Diameters of Commuting Graphs Arising from Random Skew-Symmetric Matrices

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