Matching Preclusion for Exchanged Hypercubes

Abstract

As spanning subgraphs of hypercubes, exchanged hypercubes contain less edges but maintain lots of desired properties of hypercubes. This paper considers matching preclusion, a kind of measures of edge-fault tolerance, of exchanged hypercubes EH(s, t). We show that EH(s, t) is maximally matched, that is, for s ≥ t, mp(EH(s, t)) = t + 1 and EH(s, t) is super matched if and only if (s, t) ≠ (1, 1). Comparing with results of matching preclusion for hypercubes, we conclude that exchanged hypercubes maintain the matching preclusion property of hypercubes, except for EH(1, 1).