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Let G be a finite group. The main supergraph S(G) is a graph with vertex set G in which two vertices x and y are adjacent if and only if o(x)|o(y) or o(y)|o(x). In an earlier paper, the main properties of this graph was obtained. The aim of this paper is to investigate the Hamiltonianity, Eulerianness and 2-connectedness of this graph.

SOME REMARKS ON THE ORDER SUPERGRAPH OF THE POWER GRAPH OF A FINITE GROUP