关于树图的谱半径的界

Upper Bounds on the Spectral Radius of Tree Graphs

给出了由边数为m、顶点数为n的简单连通图G生成的树图T(G)及邻树图T*(G)的谱半径的上界:ρ(T(G))≤det(Hr(G))1-1mρ(T*(G))≤det(Hr(G))1-1χ′(G)其中χ′(G)是图G的边色数;并指出当G Cn时,ρ(T(G))的上界可达。

Let G be a simple connected graph with m edges and n vertices. Denote T(G) and T~*(G) by the tree graph and the adjacent tree graph of G respectively. In this paper, the upper bounds for the spectral radius of tree graphs and adjacent tree graphs are given as follows,ρ(T(G))≤det(H_r(G))1-1mρ(T~(G))≤det(H_r(G))1-1χ′(G)where χ′(G) is the edge chromatic number of G. Moreover, when GC_n, bound of ρ(T(G)) is sharp.