Hermitian-ABC Energy Of Mixed Graphs

The study of graph energy is a very important research field in graph theory.In 1977,Gutman studied the energy of adjacency matrix of undirected graph,which has a certain application background in theoretical chemistry:through the establishment of corresponding graph model for organic molecules,the energy level and stability of organic molecules are quantitatively discussed by using the eigenvalues of graph corresponding matrix,In recent years,people mainly study the energy problems of other forms of graphs,such as the weighted energy of undirected graphs,the weighted energy of directed graphs and the weighted energy of mixed graphsThe first chapter,we introduces the research background and significance of graph energy,the related concepts of graph theory,and the research status of ABC energy and the energy of a mixed graphThe second chapter,we define the Hermitian-ABC matrix of a mixed graph,give some bounds on the Hermitian-ABC energy of a mixed graph,and characterize the relationship between the Hermitian-ABC energy of digraph D1 and D2 and the Hermitian ABC energy of the mixed graph D1?D2.Where D1?D2 is a mixed graph by adding an undirected edge between each vertex of digraph D1 and all vertices of digraph D2.The third chapter,Based on the eigenvalues of Hermiten-ABC matrix,we introduces the Hermitian-ABC Estrada index of mixed graphs.In addition,we also establish the upper and lower bounds of Hermitian-ABC Estrada index and discuss the relationship between Hermitian-ABC energy and Hermitian-ABC Estrada index.