Turkish Journal of Mathematics
Article Title
DOI
10.3906/mat-1902-61
Abstract
Let $G$ be a finite group which is not cyclic of prime power order. The join graph $\Delta(G)$ is an undirected simple whose vertices are the proper subgroups of $G$, which are not contained in the Frattini subgroup $\Phi(G)$ of $G$ and two vertices $H$ and $K$ are joined by an edge if and only if $G=\langle H,K\rangle$. We classify finite groups whose join graphs have domination number $\leq 2$ and independence number $\leq 3$. We show that $\Delta(G)\cong \Delta(A_4)$ if and only if $G\cong A_4$. We also show that if the independence number of $\Delta(G)$ is less than $15$, then $G$ is solvable; moreover, if the equality holds and $G$ is nonsolvable, then $G/\Phi(G)\cong A_5$.
Keywords
Finite group, join graph, domination number, independence number, alternating group
First Page
2097
Last Page
2113
Recommended Citation
BAHRAMI, ZAHRA and TAERI, BIJAN
(2019)
"Further results on the join graph of a finite group,"
Turkish Journal of Mathematics: Vol. 43:
No.
5, Article 2.
https://doi.org/10.3906/mat-1902-61
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss5/2
