Title of article
Planarity of Inclusion Graph of Cyclic Subgroups of Finite Group
Author/Authors
Garibbolooki, Zahra Faculty of Mathematical Sciences - Shahrood University of Technology, Shahrood, I. R. Iran , Jafari, Heidar Faculty of Mathematical Sciences - Shahrood University of Technology, Shahrood, I. R. Iran
Pages
12
From page
303
To page
314
Abstract
Let G be a finite group. The inclusion graph of cyclic subgroups of G, Ic(G), is the (undirected) graph with vertices of all cyclic subgroups of G, and two distinct cyclic subgroups ⟨a⟩ and ⟨b⟩, are adjacent if and only if ⟨a⟩ ⊂ ⟨b⟩ or ⟨b⟩ ⊂ ⟨a⟩. In this paper, we classify all finite abelian groups, whose inclusion graph is planar. Also, we study planarity of this graph for finite group G, where |π(Z(G))| ≥ 2.
Keywords
Inclusion graph , power graph , planarity , abelian group
Journal title
Mathematics Interdisciplinary Research
Serial Year
2020
Record number
2605241
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