On Graphs Associated with Character Degrees and Conjugacy Class Sizes of Direct Products of Finite Groups. Issue 1 (1st March 2015)

• Record Type: Journal Article
• Authors: Hossein-Zadeh, Samaneh; Iranmanesh, Ali; Ali Hosseinzadeh, Mohammad; Lewis, Mark L.
• Is Part Of: Canadian mathematical bulletin =. Volume 58:Issue 1(2015)
• Page Start: 105
• Page End: 109
• Publication Date: 2015-03-01
• Subjects: 20E45 -- 05C25 -- 05C76; vertex graph -- common divisor graph -- character degree -- class sizes -- graph operation; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2014-058-8
• Languages: English
• ISSNs: 0008-4395

Abstract

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.