# on removal of perfect matching from folded hypercubes

## TL;DR

This paper investigates the properties of the folded hypercube FQn, disproving a conjecture that removing a perfect matching always results in a graph isomorphic to the hypercube Qn, by providing counterexamples.

## Contribution

The paper disproves a conjecture about perfect matchings in folded hypercubes by showing counterexamples where removal does not yield a hypercube.

## Key findings

- Counterexamples to the conjecture are provided.
- Removing certain perfect matchings from FQn does not produce Qn.
- The conjecture by Dong and Wang is false in general.

## Abstract

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(In Theor. Comput. Sci.771(2019)93-98) conjectured that "A subset Em of 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.