On the conjecture of bijection between perfect matching and sub-hypercube in folded hypercubes

Abstract

Dong and Wang in [Theor. Comput. Sci. 771 (2019) 93-98] conjectured that the resulting graph of the n-dimensional folded hypercube F Q n by deleting any perfect matching is isomorphic to the hypercube Q n . In this paper, we show that the conjecture holds when n = 2, 3, and it is not true for n ≥ 4.