| With the advent of the era of informatization and intelligence,social networks have presented a complex and intricate development trend,and the stability of network security has attracted widespread attention.Therefore,it is urgent and necessary to carry out relevant research on network resilience.In the analysis and design of social networks,the spread of social influence is an important issue.If we want to consider the spread of highrisk viruses,social information,internet memes,and other things throughout the network,this process can be transformed into the burning of a graph.Graph burning is a discretetime evolution process of a graph.However,if we characterize the resilience of the network from the time perspective,the existing resilience parameters have certain limitations.Based on connectivity,which is a measure of how easy it is for a network to be destroyed,and burning number,which is a measure of the propagation speed of social influences in the network,This thesis combines the idea of burning number with connectivity and introduces a new parameter-restricted burning connectivity.Based on the restricted burning connectivity of several basic graph types such as paths,cycles,and complete bipartite graphs,mathematical programming methods are used to study the restricted burning connectivity of Cartesian product graphs,spider graphs,and caterpillar trees,and analyze the relationship between the parameter and the graph structure.By studying the structural characteristics of trees under the meaning of restricted burning connectivity,a tree restricted burning connectivity algorithm is designed,and the algorithm is implemented using the Python programming language,which verifies the correctness of the algorithm.The research shows that the restricted burning connectivity is related to the structure of the graph,the size of the residual subgraph,and the selection of the optimal fire source.This parameter can comprehensively analyze the connectivity status of the network after being damaged from the perspective of time,and can characterize the subtle differences in resilience among different networks.The research methods and conclusions of this thesis can provide theoretical basis and reference for subsequent related research. |
