On Graphs Associated with Character Degrees and Conjugacy Class Sizes of Direct Products of Finite Groups

Canadian mathematical bulletin

Mohammad Ali Hosseinzadeh¹  Samaneh Hossein-Zadeh¹  Ali Iranmanesh¹  Mark L. Lewis² 

[1] Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran;Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA

关键词: prime vertex graph;    common divisor graph;    character degree;    class sizes;    graph operation;   

DOI  :  10.4153/CMB-2014-058-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

The prime vertex graph, $Delta (X)$, and the common divisor graph,$Gamma (X)$, are two graphs that have been defined on a set ofpositive integers $X$. Someproperties 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 ofconjugacy class sizes of a group. In this paper, we gather someresults on these graphs arising in the context of direct product oftwo groups.

【 授权许可】

Unknown