2021
DOI: 10.48550/arxiv.2104.10867
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Forbidden subgraphs in generating graphs of finite groups

Abstract: Let G be a 2-generated group. The generating graph Γ(G) is the graph whose vertices are the elements of G and where two vertices g 1 and g 2 are adjacent if G = g 1 , g 2 . This graph encodes the combinatorial structure of the distribution of generating pairs across G. In this paper we study some graph theoretic properties of Γ(G), with particular emphasis on those properties that can be formulated in terms of forbidden induced subgraphs. In particular we investigate when the generating graph Γ(G) is a cograph… Show more

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