The Study Of The ISI Energy And Harmonic Energy Of Graphs

Graph energy is an important research area in graph spectrum theory.Since 1977,chemist Gutman proposed the graph energy,especially the characterization of the graph energy,the influence of edge deletion or adding edges on the graph energy,has become a research hotspot in graph theory.Here we study the ISI energy and Harmonic energy of graphs by combining graph invariants and topological exponents.The first chapter introduces the topological index,research background,significance and related concepts and definitions,and briefly describes the research status of ISI energy and Harmonic energy.In the second chapter,we optimize the ISI spectral radius and the ISI energy by using some familiar inequalities(such as Cauchy-Schwarz inequality),the maximum,minimum and edge degree of the graph,and obtain some new bounds and give the corresponding extreme value graph.In the third chapter,we study the changes of the Harmonic energy of the graph after the deletion of a non-hanging edge and obtain the corresponding upper bound.Then,using the definitions and properties of the Harmonic energy and the graph transformations,we prove that the path graph P_n has the maximum Harmonic energy in the coral tree set T(n).