Abstract
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 [Formula: see text], the generalized quaternion groups [Formula: see text], the quasi-dihedral groups [Formula: see text] and the modular groups [Formula: see text]. 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.
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