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, $|\pi (G)|\leq 8$. 
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     author = {Lucido, Maria Silvia},
     title = {Groups in which the prime graph is a tree},
     journal = {Bollettino della Unione matematica italiana},
     pages = {131--148},
     publisher = {mathdoc},
     volume = {Ser. 8, 5B},
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     year = {2002},
     zbl = {1097.20022},
     mrnumber = {MR1881928},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_1_a5/}
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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/