Investigation Of Total Graph Coherent Configurations For Strongly Regular Graphs

Association scheme theory is an important branch of algebraic combinatorics.Therefore,the study of association scheme construction method constitutes an important part of the research.Higman generalized the concept of association scheme and introduced the concept of coherent configuration.The orbits of arbitrary permutation group acting on the ? × ? form into an association scheme or coherent configuration.Each orbit is recorded as an associate class or a basic relation,and a new association scheme can be obtained by combining the basic relation of the coherent configuration.In this paper,we use this method of constructing the association scheme to study from the following sections.The introduction chapter mainly introduces the research background and status of the total graph coherent configurations of strongly regular graphs.The first chapter mainly introduces the definition of association scheme,coherent configuration,coherent closure and so on.Chapter two introduce the structure of the total graph coherent configurations of strongly regular graphs.Through computer algebra software,the basic relationship of coherent configuration can be obtained.Then,we build new association schemes by combining the basic relations of the configuration.Finally,we analyze the relationship between the coherent closure of each kind of strong regular graph and the total graph coherent configurations.