@article {
author = {Abdolghafourian, Adeleh and Iranmanesh, Mohammad Ali},
title = {On the number of connected components of divisibility graph for certain simple groups},
journal = {Transactions on Combinatorics},
volume = {5},
number = {2},
pages = {33-40},
year = {2016},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2016.8595},
abstract = {The divisibility graph $\mathscr{D}(G)$ for a finite group $G$ is a graph with vertex set $cs(G)\setminus\{1\}$ where $cs(G)$ is the set of conjugacy class sizes of $G$. Two vertices $a$ and $b$ are adjacent whenever $a$ divides $b$ or $b$ divides $a$. In this paper we will find the number of connected components of $\mathscr{D}(G)$ where $G$ is a simple Zassenhaus group or an sporadic simple group.},
keywords = {Divisibility graph,connected component,Simple groups},
url = {https://toc.ui.ac.ir/article_8595.html},
eprint = {https://toc.ui.ac.ir/article_8595_8e231b4595dc014a92b1ce8c12a9732f.pdf}
}