Abstract
Let G be a graph on n vertices. Denote by f(G) the minimum size of a matching M in G such that M is uniquely extendable to a perfect matching in G. The prism of G is defined as G□K2, that is, the Cartesian product of G with the complete graph on 2 vertices. Assume that there exists an involutory matrix A with zero diagonal such that the graph described by the zero/non-zero pattern of off-diagonal entries of A is isomorphic to G. It is shown that f(G□K2)=n2 if G is bipartite. This generalizes a known result. The quantity f for prisms of some families of graphs are determined.
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