Planarity of Inclusion Graph of Cyclic Subgroups of Finite Group

Document Type : Original Scientific Paper

Authors

Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, I. R. Iran

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

References

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Mathematics Interdisciplinary Research
Volume 5, Issue 4
December 2020
Pages 303-314

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