Geodesic
Groups in which the prime graph is a tree
Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 1, pp. 131-148.

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The prime graph $\Gamma(G)$ of a finite group $G$ is defined as follows: the set of vertices is $\pi(G)$, the set of primes dividing the order of $G$, and two vertices $p$, $q$ are joined by an edge (we write $p\sim q$) if and only if there exists an element in $G$ of order $pq$. We study the groups $G$ such that the prime graph $\Gamma(G)$ is a tree, proving that, in this case, $|\pi (G)|\leq 8$.
Il «prime graph» $\Gamma(G)$ di un gruppo finito $G$ è definito nel modo seguente: l'insieme dei vertici è $\pi(G)$, cioè l'insieme dei primi che dividono l'ordine del gruppo e due vertici $p$, $q$ costituiscono un lato (e si indica $p\sim q$) se esiste un elemento in $G$ di ordine $pq$. Si studiano i gruppi $G$ tali che il grafo $\Gamma(G)$ è un albero, dimostrando che, in questo caso, $|\pi (G)|\leq 8$. 
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Lucido, Maria Silvia. Groups in which the prime graph is a tree. Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 1, pp. 131-148. http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_1_a5/

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