ON THE ANTI-FORCING NUMBER OF GRAPHS

Abstract. Let G = (V, E) be a simple connected graph. A perfect matching (or Kekul´e structure in chemical literature) 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 and study their anti-forcing numbers.