ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS
Let $G$ be a non-abelian finite group. In this paper, we prove that $Gamma(G)$ is $K_4$-free if and only if $G cong A times P$, where $A$ is an abelian group, $P$ is a $2$-group and $G/Z(G) cong mathbb{ Z}_2 times mathbb{Z}_2$. Also, we show that $Gamma(G)$ is $K_{1,3}$-free if and only if $G cong {...
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Shahrood University of Technology
2015-02-01
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| Series: | Journal of Algebraic Systems |
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| Online Access: | http://jas.shahroodut.ac.ir/article_372_7f1845805d519f0e1594759c85b7ed9d.pdf |
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doaj-11c33723a5a3461c8f9532f28dc370142020-11-25T03:37:03ZengShahrood University of TechnologyJournal of Algebraic Systems2345-51282345-511X2015-02-012214715110.22044/jas.2015.372372ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHSNeda Ahanjideh0Hajar Mousavi1Shahrekord Univ.Shahrekord UniversityLet $G$ be a non-abelian finite group. In this paper, we prove that $Gamma(G)$ is $K_4$-free if and only if $G cong A times P$, where $A$ is an abelian group, $P$ is a $2$-group and $G/Z(G) cong mathbb{ Z}_2 times mathbb{Z}_2$. Also, we show that $Gamma(G)$ is $K_{1,3}$-free if and only if $G cong {mathbb{S}}_3,~D_8$ or $Q_8$.http://jas.shahroodut.ac.ir/article_372_7f1845805d519f0e1594759c85b7ed9d.pdfnon-commuting graph$K_4$-free graph$K_{13}$-free graph |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Neda Ahanjideh Hajar Mousavi |
| spellingShingle |
Neda Ahanjideh Hajar Mousavi ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS Journal of Algebraic Systems non-commuting graph $K_4$-free graph $K_{1 3}$-free graph |
| author_facet |
Neda Ahanjideh Hajar Mousavi |
| author_sort |
Neda Ahanjideh |
| title |
ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS |
| title_short |
ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS |
| title_full |
ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS |
| title_fullStr |
ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS |
| title_full_unstemmed |
ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS |
| title_sort |
on the groups with the particular non-commuting graphs |
| publisher |
Shahrood University of Technology |
| series |
Journal of Algebraic Systems |
| issn |
2345-5128 2345-511X |
| publishDate |
2015-02-01 |
| description |
Let $G$ be a non-abelian finite group. In this paper, we prove that $Gamma(G)$ is $K_4$-free if and only if $G cong A times P$, where $A$ is an abelian group, $P$ is a $2$-group and $G/Z(G) cong mathbb{ Z}_2 times mathbb{Z}_2$. Also, we show that $Gamma(G)$ is $K_{1,3}$-free if and only if $G cong {mathbb{S}}_3,~D_8$ or $Q_8$. |
| topic |
non-commuting graph $K_4$-free graph $K_{1 3}$-free graph |
| url |
http://jas.shahroodut.ac.ir/article_372_7f1845805d519f0e1594759c85b7ed9d.pdf |
| work_keys_str_mv |
AT nedaahanjideh onthegroupswiththeparticularnoncommutinggraphs AT hajarmousavi onthegroupswiththeparticularnoncommutinggraphs |
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1724547399465041920 |