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On Graphs Associated with Character Degrees and Conjugacy Class Sizes of Direct Products of Finite Groups
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2015
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