The structure and metric dimension of the power graph of a finite group

DOI10.1016/j.ejc.2014.08.019zbMath1301.05142OpenAlexW1991651976MaRDI QIDQ458587

Kaishun Wang, Min Feng, Xuan Long Ma

Publication date: 8 October 2014

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

Full work available at URL: https://doi.org/10.1016/j.ejc.2014.08.019

zbMATH Keywords

perfect graphmetric dimension of the power graph of a cyclic group

Mathematics Subject Classification ID

Perfect graphs (05C17)

Related Items (47)

Prime index elements graph of a group ⋮ On the power graphs of certain finite groups ⋮ Forbidden subgraphs in reduced power graphs of finite groups ⋮ The rainbow connection number of the power graph of a finite group ⋮ Finite groups with the same power graph ⋮ Automorphism groups of supergraphs of the power graph of a finite group ⋮ On connectedness of power graphs of finite groups ⋮ A survey on enhanced power graphs of finite groups ⋮ On the minimum degree, edge-connectivity and connectivity of power graphs of finite groups ⋮ Finite groups whose intersection power graphs are toroidal and projective-planar ⋮ The power index of a graph ⋮ Perfect codes in power graphs of finite groups ⋮ On the order supergraph of the power graph of a finite group ⋮ Getting the Lay of the Land in Discrete Space: A Survey of Metric Dimension and Its Applications ⋮ Power graphs of all nilpotent groups ⋮ The full automorphism group of the power (di)graph of a finite group ⋮ Vertex connectivity of the power graph of a finite cyclic group II ⋮ Connectivity of superpower graphs of some non-abelian finite groups ⋮ A study of enhanced power graphs of finite groups ⋮ On the independence number of the power graph of a finite group ⋮ The strong metric dimension of the power graph of a finite group ⋮ Perfect codes in proper reduced power graphs of finite groups ⋮ Finite groups whose noncyclic graphs have positive genus ⋮ Characterization of groups with planar, toroidal or projective planar (proper) reduced power graphs ⋮ Power graphs of (non)orientable genus two ⋮ The power graph of a torsion-free group determines the directed power graph ⋮ Strong metric dimensions for power graphs of finite groups ⋮ The complement of proper power graphs of finite groups ⋮ Finite groups with star-free noncyclic graphs ⋮ Automorphism group and other properties of zero component graph over a vector space ⋮ An Euler totient sum inequality ⋮ Lambda number of the power graph of a finite group ⋮ Fixing number and metric dimension of a zero-divisor graph associated with a ring ⋮ The metric dimension of the enhanced power graph of a finite group ⋮ On the commuting graph of semidihedral group ⋮ Proper connection of power graphs of finite groups ⋮ On the minimum degree of the power graph of a finite cyclic group ⋮ Exchange property for resolving sets in power graphs ⋮ On the metric dimension of the reduced power graph of a finite group ⋮ Hamiltonian cycles of power graph of abelian groups ⋮ 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 ⋮ Power graphs and exchange property for resolving sets ⋮ The automorphism group and fixing number of orthogonality graph over a vector space ⋮ On the minimum degree of power graphs of finite nilpotent groups ⋮ On the chromatic number of the power graph of a finite group

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