On The Minimal Distance Spectral Radius Of Tree With Given Maximal Degree

The theory of Graph Spectra is an important part of Graph theory.There are all kinds of matrices introduced to represent graphs.It is the main content of Graph Spectra to study the topological properties of graphs by the algebraic properties of matrices.In this paper,we discuss a hot problem of Graph Spectra,namely we investigate the spectral radius of distance matrix of graphs and extreme graph.The main contents of this paper are as follows:1.We introduce some important concepts of Graph Spectra and research background.2.Some common transformations of graphs used in the study of distance spectral radius and some related knowledge of matrices are gived.3.Some new transformations of graphs and investigate change rules of distance spectral radius of graphs are proposed.4.We determine the graphs having the minimum distance spectral radius among all trees of the maximal degree ? with [n/2]???n-1.5.We characterize the graphs having the minimum distance spectral radius among all trees with perfect matchings and maximal degree ? satisfying [n/2]+1???m.