Distance Eigenvalue Problems For Three Kinds Of Special Graphs

The study of the distance eigenvalue of special graphs plays an important role in network fiow algorithm,graph embedding theory and molecular stability.In this paper,we study the distance eigenvalue of four-leaf graph,corona graphs of Kn o Km· and Ir(Kn).In chapter 1,we introduce the background of graph theory,and the relevant definitions of graph theory.We also introduce the development of the distance matrix,the distance Laplacia--n matrix and the distance signless Laplacian matrix of graphs.In chapter 2,in order to study the changes of the two maximum eigenvalues sum of the three kinds of distance matrices of four-leaf graph,we give two transformations of four-leaf graph.In chapter 3,we study the distance spectral radius,the distance Laplacian spectral radius and distance signless Laplacian spectral radius of two corona graphs of Kn o Km and Ir(Kn).And we give three kinds of distance energy of Kn o Km and Ir(Kn).