Changes in binding number and binding degree of a graph under different edge operations

Abstract

The binding number of a graph \(G\) is defined as \(\operatorname{bind}(G)=\min \left\{\frac{N(X) \mid}{|X|}: X \subseteq V(G), X \neq \emptyset\right.\) and \(\left.N(X) \neq V(G)\right\}\). In this paper we consider the effects of contraction, deletion and/or addition of an edge on the binding number of a graph. Also, invariance of binding number is considered under these operations. A new parameter is defined here, named the binding degree. The variations of binding degree under different edge operations is also considered.