Open AccessOn diameters estimations of the commuting graphs of Sylow $p$-subgroups of the symmetric groups
Author(s) -
Yu. Yu. Leshchenko,
L. V. Zoria
Publication year - 2013
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.5.1.70-78
Subject(s) - mathematics , sylow theorems , social connectedness , combinatorics , graph , discrete mathematics , group (periodic table) , finite group , chemistry , psychology , organic chemistry , psychotherapist
The commuting graph of a group $G$ is an undirected graph whose vertices are non-central elements of $G$ and two distinct vertices $x,y$ are adjacent if and only if $xy=yx$. This article deals with the properties of the commuting graphs of Sylow $p$-subgroups of the symmetric groups. We define conditions of connectedness of respective graphs and give estimations of the diameters if graph is connected.