Geodesic
On Graphs Associated with Character Degrees and Conjugacy Class Sizes of Direct Products of Finite Groups
Canadian mathematical bulletin, Tome 58 (2015) no. 1, pp. 105-109

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DOI

The prime vertex graph, $\Delta \left( X \right)$ , and the common divisor graph, $\Gamma \left( X \right)$ , are two graphs that have been defined on a set of positive integers $X$ . Some properties of these graphs have been studied in the cases where either $X$ is the set of character degrees of a group or $X$ is the set of conjugacy class sizes of a group. In this paper, we gather some results on these graphs arising in the context of direct product of two groups.
DOI : 10.4153/CMB-2014-058-8
Mots-clés : 20E45, 05C25, 05C76, vertex graph, common divisor graph, character degree, class sizes, graph operation 
Hossein-Zadeh, Samaneh; Iranmanesh, Ali; Hosseinzadeh, Mohammad Ali; Lewis, Mark L. On Graphs Associated with Character Degrees and Conjugacy Class Sizes of Direct Products of Finite Groups. Canadian mathematical bulletin, Tome 58 (2015) no. 1, pp. 105-109. doi: 10.4153/CMB-2014-058-8
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     title = {On {Graphs} {Associated} with {Character} {Degrees} and {Conjugacy} {Class} {Sizes} of {Direct} {Products} of {Finite} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {105--109},
     year = {2015},
     volume = {58},
     number = {1},
     doi = {10.4153/CMB-2014-058-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-058-8/}
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