Survey of equi-integrity value in graphs

In a communication network vulnerability is the resistance of the graph after disruption of some center or connections. The communication network can be modeled as a graph. There is different parameters to investigate vulnerability. Some of them are connectivity, integrity, toughness, scattering, tenacity, rupture degree and equi-integrity. These parameters are related with disrupted centers and connections. Later on some other parameters defined to take into account neighborhood of centers and connections. These parameters are neighbor connectivity, neighbor integrity, neighbor scattering number and neighbor rupture degree. This thesis consist of five chapters. In the first chapter history of Graph Theory is given. In the second chapter fundamental definitions and types of graphs are given. In the third chapter definition of equi-integrity and the previously calculated equi-integrity value of some special graphs are given. In the fourth chapter equi-integrity of some well-known graphs are calculated and definition of neighbor equi-integrity which is defined by equi-integrity and vertex neighbor integrity are given. In the last part conclusions and suggestions obtained from that study are given.