Geodesic
Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups
Algebra and discrete mathematics, Tome 18 (2014) no. 1, pp. 42-49

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The power graph of a finite group is the graph whose vertices are the elements of the group and two distinct vertices are adjacent if and only if one is an integral power of the other. In this paper we discuss the planarity and vertex connectivity of the power graphs of finite cyclic, dihedral and dicyclic groups. Also we apply connectivity concept to prove that the power graphs of both dihedral and dicyclic groups are not Hamiltonian.
Keywords: power graph, connectivity, planarity, cyclic group, dihedral group
Mots-clés : dicyclic group. 
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     title = {Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups},
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     url = {http://geodesic.mathdoc.fr/item/ADM_2014_18_1_a5/}
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Sriparna Chattopadhyay; Pratima Panigrahi. Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups. Algebra and discrete mathematics, Tome 18 (2014) no. 1, pp. 42-49. http://geodesic.mathdoc.fr/item/ADM_2014_18_1_a5/