A Study Of P-edge Neighbor Invulnerability Of Networks

Human have entered the era of networking,which has attracted increasing attention to the research of network invulnerability.As research deepens,it has been found that existing non-neighbor and neighbor invulnerability parameters have significant shortcomings in characterizing network invulnerability.When an edge in a network fails,its adjacent edges fail with probability p.Therefore,the study of network invulnerability in p-neighbor scenarios has more practical significance.In this thesis,inspired by the neighbor and non-neighbor invulnerability parameters and combined with the edge failure probability p,two new parameters are introduced to describe the invulnerability of the network,namely,the p-edge neighbor scattering number and p-edge neighbor connectivity,the formulas for calculating p-edge neighbor scattering number of some basic graphs and some combined star graphs,and the formulas for calculating p-edge neighbor connectivity of some basic graphs and unicyclic graphs with diameter 3 are given,the algorithm for calculating the p-edge neighbor scattering number of star tree is designed and corresponding examples are given.On this basis,the relationship between the p-edge neighbor scattering number and its edge number is explored,and the relationship between the p-edge neighbor scattering number,the p-edge neighbor connectivity,the structure of the graph and the edge failure probability p is deeply studied.By comparing the existing p-neighbor invulnerability parameters,the subtle differences between the two new parameters in describing the invulnerability of networks are described.The research of this thesis shows that the two new parameters based on the invulnerability of the p-edge neighbor can better describe the invulnerability of the network,which has an important fundamental role for the related research.