The average binding number of graphs and its algorithm

TL;DR

This paper investigates the average binding number of graphs, establishes bounds for specific graph types, and introduces algorithms for calculating this parameter, demonstrating their effectiveness through analysis.

Contribution

It provides new bounds for the average binding number of certain graphs and develops algorithms to compute this parameter efficiently.

Findings

Bounds for average binding number of special graphs are derived.

Algorithms for calculating average binding numbers are developed and analyzed.

Algorithms are validated through code metrics and practical usefulness.

Abstract

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. In this paper, some bounds of 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.