The Order Supergraph of the Power Graph of a Finite Group

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The power graph P(G) is a graph with group elements as vertex set and two elements are adjacent if one is a power of the other. The order supergraph S(G) of the power graph P(G) is a graph with vertex set G in which two elements x, y ∈ G are joined if o(x) | o(y) or o(y) | o(x). The purpose of this paper is to study certain properties of this new graph together with the relationship between P(G) and S(G).