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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

Samaneh Hossein-Zadeh ,
Ali Iranmanesh ,
Mohammad Ali Hosseinzadeh  and
Mark L. Lewis
Samaneh Hossein-Zadeh
Affiliation:
Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran. e-mail: hosseinzadeh.samaneh@yahoo.com, e-mail: iranmanesh@modares.ac.ir e-mail: ma.hoseinzade@gmail.com
Ali Iranmanesh
Affiliation:
Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran. e-mail: hosseinzadeh.samaneh@yahoo.com, e-mail: iranmanesh@modares.ac.ir e-mail: ma.hoseinzade@gmail.com
Mohammad Ali Hosseinzadeh
Affiliation:
Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran. e-mail: hosseinzadeh.samaneh@yahoo.com, e-mail: iranmanesh@modares.ac.ir e-mail: ma.hoseinzade@gmail.com
Mark L. Lewis
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA. e-mail: lewis@math.kent.edu
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Abstract

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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.

Keywords

20E4505C2505C76vertex graphcommon divisor graphcharacter degreeclass sizesgraph operation
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 1 , 01 March 2015 , pp. 105 - 109
Copyright
Copyright © Canadian Mathematical Society 2015

References

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