Matching Preclusion for the Shuffle-Cubes

Abstract

The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. A graph is maximally matched if its matching preclusion number is equal to its minimum degree, and is super matched if the matching preclusion number can only be achieved by deleting all edges incident to a single vertex. In this paper, we determine the matching preclusion number and classify the optimal matching preclusion sets for the shuffle-cube graphs, a variant of the well-known hypercubes.