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on removal of perfect matching from folded hypercubes

The hypercube Qn of dimension n is one of the most versatile and powerful interconnection networks. The n−dimensional folded cube denoted as FQn, a variation of the hypercube possesses some embeddable properties that the hypercube does not possess. Dong and Wang[2](In Theor. Comput. Sci.771(2019)93− 98) conjectured that ”A subset Em of 2n − 1 edges of FQn is a perfect matching if and only if FQn −Em is isomorphic to Qn”. In this paper, we disprove this conjecture by providing some perfect matchings removal of which from FQn do not give a graph isomorphic to Qn.