TY - JOUR
ID - 573
TI - On the planarity of a graph related to the join of subgroups of a finite group
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Taeri, B.
AU - Ahmadi, H.
AD - Isfahan University of Technology
Y1 - 2014
PY - 2014
VL - 40
IS - 6
SP - 1413
EP - 1431
KW - Graph on group
KW - plannar graph
KW - finite group
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_573.html
L1 - http://bims.iranjournals.ir/article_573_026d933a1762fba8b0e0f563507e5038.pdf
ER -