ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS
Copyright policy )ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS
Summary: 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 \(Q_8\).
- Shahrekord University Iran (Islamic Republic of)
\(K_4\)-free graph, $K_4$-free graph, QA1-939, $K_{1, 3}$-free graph, non-commuting graph, \(K_{1, 3}\)-free graph, Mathematics, Arithmetic and combinatorial problems involving abstract finite groups, Graphs and abstract algebra (groups, rings, fields, etc.)
\(K_4\)-free graph, $K_4$-free graph, QA1-939, $K_{1, 3}$-free graph, non-commuting graph, \(K_{1, 3}\)-free graph, Mathematics, Arithmetic and combinatorial problems involving abstract finite groups, Graphs and abstract algebra (groups, rings, fields, etc.)
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