The Distance Spectrum Of Some Kinds Of Graphs

In this paper, we mainly study a hot topic in the theory of Graph Spectra, that is the extreme graph of the distance spectrum. In this paper, we firstly introduce the involvement of distance spectrum problem at home and abroad, then we discuss our problems by the following three aspects:1. Let (?)(n, d) be the set of all trees with both n vertices and given diameter d. In this paper, we consider the distance spectral radii of the trees with given diameter and determine that the tree with minimal distance spectral radius among all graphs in (?)(n, d) is a caterpillar whose pendent vertices outside the diameter path are all adjacent with its center vertex;2. We find the graph with the minimal distance spectrum radius among all the∞-type bicyclic graphs, also present a conjecture about normal bicyclic graph;3. We find the graph with the maximal distance spectrum radius among all the bicyclic graphs.