@article {
author = {Taeri, B. and Ahmadi, H.},
title = {On the planarity of a graph related to the join of subgroups of a finite group},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {40},
number = {6},
pages = {1413-1431},
year = {2014},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {Let $G$ be a finite group which is not a cyclic $p$-group, $p$ a prime number. We define an undirected simple graph $Delta(G)$ whose vertices are the proper subgroups of $G$, which are not contained in the Frattini subgroup of $G$ and two vertices $H$ and $K$ are joined by an edge if and only if $G=langle H , Krangle$. In this paper we classify finite groups with planar graph. %For this, by Kuratowski's Theorem, we have to study subdivisions %of the Kuratowski graphs $K_{3 , 3}$ and $K_5$ in the graph $Delta(G)$. Our result shows that only few groups have planar graphs.},
keywords = {Graph on group,plannar graph,finite group},
url = {http://bims.iranjournals.ir/article_573.html},
eprint = {http://bims.iranjournals.ir/article_573_026d933a1762fba8b0e0f563507e5038.pdf}
}