Strong matching preclusion under the conditional fault model

Strong matching preclusion that additionally permits more destructive vertex faults in a graph [J.-H. Park, I. Ihm, Strong matching preclusion, Theoretical Computer Science 412 (2011) 6409–6419] is an extended form of the original matching preclusion that assumes only edge faults [R.C. Brigham, F. Harary, E.C. Violin, J. Yellen, Perfect-matching preclusion, Congressus Numerantium 174 (2005) 185–192]. In this paper, we study the problem of strong matching preclusion under the condition that no isolated vertex is created as a result of faults. After briefly discussing some fundamental classes of graphs in the point of the conditional matching preclusion, we establish the conditional strong matching preclusion number for the class of restricted hypercube-like graphs, which include most nonbipartite hypercube-like networks found in the literature.