Edge-maximality of power graphs of finite cyclic groups

DOI10.1007/s10801-013-0490-5zbMath1303.05084arXiv1311.2984OpenAlexW2149423530MaRDI QIDQ478350

G. R. Pourgholi, Curtin, Brian

Publication date: 3 December 2014

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

Full work available at URL: https://arxiv.org/abs/1311.2984

zbMATH Keywords

cyclic group\(p\)-groupgreatest prime divisorleast prime divisor

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (27)

On the power graphs of certain finite groups ⋮ The power graph of a torsion-free group of nilpotency class 2 ⋮ Laplacian spectra of power graphs of certain prime-power Abelian groups ⋮ Matching in power graphs of finite groups ⋮ On connectedness of power graphs of finite groups ⋮ On the minimum degree, edge-connectivity and connectivity of power graphs of finite groups ⋮ On the characteristic polynomial of power graphs ⋮ The extreme vertices of the power graph of group \(S_n\) ⋮ Vertex connectivity of the power graph of a finite cyclic group II ⋮ Degree and distance based topological descriptors of power graphs of finite non-abelian groups ⋮ On the number of edges of cyclic subgroup graphs of finite groups ⋮ The Spectra of power graphs of certain finite groups ⋮ On the power graph and the reduced power graph of a finite group ⋮ Vertex connectivity of the power graph of a finite cyclic group ⋮ An Euler totient sum inequality ⋮ A combinatorial characterization of finite groups of prime exponent ⋮ The number of edges in power graph of finite groups ⋮ On the minimum degree of the power graph of a finite cyclic group ⋮ Laplacian spectra of power graphs of certain finite groups ⋮ Ideal basis in constructions defined by directed graphs ⋮ Minimal cut-sets in the power graphs of certain finite non-cyclic groups ⋮ On the enhanced power graph of a finite group ⋮ Recent developments on the power graph of finite groups – a survey ⋮ A note on the power graphs of finite nilpotent groups ⋮ Spectrum and L-spectrum of the power graph and its main supergraph for certain finite groups ⋮ Spectrum of proper power graphs of the direct product of certain finite groups ⋮ On the chromatic number of the power graph of a finite group

Cites Work

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• The power graph of a finite group
• Groups of prime power order. Vol. 1.
• Directed graphs and combinatorial properties of semigroups
• Undirected power graphs of semigroups
• Power graphs and semigroups of matrices
• On the power graph of a finite group
• The power graph of a finite group, II
• Sums of Element Orders in Finite Groups
• Power graphs: A survey

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