About the average binding number of networks

As a result of the interaction of rapid development and competition in information technologies, the reliability of a network and how solid it remains is important. It is called the hat vulnerability of the network to measure the endurance of the network until communication is interrupted by the deterioration of the connection lines between some centers or centers in a network. The centers of the network can be modeled such that the vertex of the network and the connecting lines are the distances of the graph, while investigating the strength of a communication network against disturbances that may occur in the centers or connecting lines. Networks can be modeled with graphs and there are several parameters to measure the vulnerability of these graphs. In this study, the average binding number was studied. For v∈V(G), the local binding number of v is bind(G)=min(s∈Fv (G)){(|N(S)|)/(|S|)}, where Fv(G)={S⊆V(G)|v∈S,S≠∅,N(S)≠V(G)}. Furthermore, the average binding number of G is defined as bindav (G)=1/n ∑ (v∈V(G) bindv(G), where n is the number of vertices in graph G. In this paper, some bounds of the average binding number are given. The average binding number of some special graphs are obtained. Finally, the algorithm for calculation of average binding numbers of graphs is given. The algorithms of these parameters are developed that calculates for any graph and the algorithms are explained. The algorithms are analyzed by code metrics and their usefulness is shown.