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Permutability graphs of subgroups of some finite non-abelian groups. (English) Zbl 1346.05116

Summary: In this paper, we study the structure of the permutability graphs of subgroups, and the permutability graphs of non-normal subgroups of the following groups: the dihedral groups \(D_n\), the generalized quaternion groups \(Q_n\), the quasi-dihedral groups \(QD_{2^n}\) and the modular groups \(M_{p^n}\). Further, we investigate the number of edges, degrees of the vertices, independence number, dominating number, clique number, chromatic number, weakly perfectness, Eulerianness, Hamiltonicity of these graphs.

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C07 Vertex degrees
05C15 Coloring of graphs and hypergraphs
05C45 Eulerian and Hamiltonian graphs
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
20K27 Subgroups of abelian groups
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References:

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