Anti–Forcing Number of Some Specific Graphs

Let G be a simple connected graph. A perfect matching (or Kekulé structure in chemical language) of G is a set of disjoint edges which covers all vertices of G. The anti–forcing number of G is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching and is denoted by af(G). In this paper we consider some specific graphs that are of importance in chemistry and study their anti–forcing numbers.