Abstract
AbstractThe power graph \(\mathcal{G}(G)\) of a finite group G is the graph with vertex set G, having an edge joining x and y whenever one is a power of the other. In this paper we study some properties of \(\mathcal{G}(S_{n})\) and \(\mathcal{G}(D_{n})\), (n ≥ 3), where S n and D n are the symmetric group on n letters and dihedral group of degree n respectively. Finally we discuss the details about the power graphs of finite non-abelian groups of order up to 14.KeywordsGroupEuler’s φ functionPower graphPlanar graphEulerian graphChromatic number of a graph
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