Study On Some Generalized Strongly Regular Graphs With Special Parameters

In 1963,Bose introduced the definition of strongly regular graph.The generalized strongly regular graph is a new generalization of strongly regular graph,In 2017,Huo Lijun and Zhang Gengsheng first proposed the generalized strongly regular graph,and proved that some subconstituents of a family of finite geometric graphs are exactly gen-eralized strongly regular graphs.A A k-regular graph G on n vertices is called a generalized strongly regular graph of grade p if the number of common neighbours of both any two adjacent vertices and any two non-adjacent vertices takes on p distinct values.In this paper,we investigate the existence of some generalized strongly regular graphs with special parameters of grade 2,and the line graphs of generalized strongly regular graphs of grade 2 with parameters(n,k;k-2,k-3;k,k-1).The general arrangement is as follows:In Chapter 1,we introduce some preliminary knowledge,a relationship between the parameters of semi-strongly regular graphs,and some conclusions that to be used in the following research process.In Chapter 2,we study the existence of some generalized strongly regular graphs of grade 2 with special parameters.In Chapter 3,we list some generalized strongly regular graphs of grade 2 and grade 3 with up to 13 vertices.In Chapter 4,we study the line graphs of generalized strongly regular graphs of grade 2 with parameters(n,k;k-2,k-3;k,k-1).The results obtained in this paper partially solve the problem of the existence of the generalized strongly regular graphs.