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- W4320351105 abstract "Let $G$ be a $2$-generated group. The generating graph $Gamma(G)$ is the graph whose vertices are the elements of $G$ and where two vertices $g_1$ and $g_2$ are adjacent if $G = langle g_1, g_2 rangle.$ This graph encodes the combinatorial structure of the distribution of generating pairs across $G.$ In this paper we study some graph theoretic properties of $Gamma(G)$, with particular emphasis on those properties that can be formulated in terms of forbidden induced subgraphs. In particular we investigate when the generating graph $Gamma(G)$ is a cograph (giving a complete description when $G$ is soluble) and when it is perfect (giving a complete description when $G$ is nilpotent and proving, among the others, that $Gamma(S_n)$ and $Gamma(A_n)$ are perfect if and only if $nleq 4$). Finally we prove that for a finite group $G$, the properties that $Gamma(G)$ is split, chordal or $C_4$-free are equivalent." @default.
- W4320351105 created "2023-02-13" @default.
- W4320351105 creator A5067214307 @default.
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- W4320351105 date "2021-04-22" @default.
- W4320351105 modified "2023-09-28" @default.
- W4320351105 title "Forbidden subgraphs in generating graphs of finite groups" @default.
- W4320351105 doi "https://doi.org/10.48550/arxiv.2104.10867" @default.
- W4320351105 hasPublicationYear "2021" @default.
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