Given a finite group G, the generating graph Γ(G) of G has as vertices the non-identity elements of G, and two vertices are adjacent if and only if they are distinct and generate G as group elements. Let G be a 2-generated finite group. We prove that Γ(G) is planar if and only if G is isomorphic to one of the following groups: C2, C3, C4, C5, C6, C2 × C2, D3, D4, Q8, C4 × C2, D6 .
Finite groups with planar generating graph
Lucchini A.
2020
Abstract
Given a finite group G, the generating graph Γ(G) of G has as vertices the non-identity elements of G, and two vertices are adjacent if and only if they are distinct and generate G as group elements. Let G be a 2-generated finite group. We prove that Γ(G) is planar if and only if G is isomorphic to one of the following groups: C2, C3, C4, C5, C6, C2 × C2, D3, D4, Q8, C4 × C2, D6 .File in questo prodotto:
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