The concept of the binding number of a graph was introduced by Woodall in 1973. In this paper w e characterize the set F, of all pairs (a, b ) of integers such that there is a graph G with n vertices and binding number alb that has a realizing set of b vertices.
BINDING NUMBERS OF CERTAIN SPECIAL GRAPHSDefinition. (Woodall [2]) Let V = V(G) denote the set of vertices and E = E(G) the set of edges of the graph G. For x E V(G) let T ( x ) denote the set of all vertices of G which are adjacent to x. For X C V(G) let T(X) = UxaT(X). Let S(G) = {XI fl Z X C V(G), r(X) # V(G)). Then the binding number, bind(G), of G is bind(G) = min I T ( X ) I / I XI . X € 6 ( G )We introduce the term "realizing set" for a set X E S(G) such that bind(G)= I r(x>l /IXl.
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