Let $ G $ be a group and let $T^{3}(G)$ be the proper subgroup $\lbrace h\in G \vert (gh)^{3}=(hg)^{3},~for~all~ g\in G\rbrace $ of $ G $. \textit{The third-noncommuting graph} of $ G $ is the graph with vertex set $ G\setminus T^{3}(G) $, where two vertices $ x $ and $ y $ are adjacent if $ (xy)^{3}\neq (yx)^{3} $. In this paper, at first we obtain some results for this graph for any group $G$. Then, we investigate the structure of this graph for some groups.
@article{23517,
title = {The Third-Noncommuting Graph of a Group},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {34},
year = {2015},
doi = {10.5269/bspm.v34i1.23517},
language = {EN},
url = {http://dml.mathdoc.fr/item/23517}
}
Zallaghi, Maysam; Iranmanesh, Ali. The Third-Noncommuting Graph of a Group. Boletim da Sociedade Paranaense de Matemática, Tome 34 (2015) . doi : 10.5269/bspm.v34i1.23517. http://gdmltest.u-ga.fr/item/23517/