关于图与其补图谱半径之和的又一上界

Another Upper Bounds on Sum of the Spectral Radius of a Graph and Its Complement

给出了图与其补图谱半径之和ρ(G)+ρ(Gc)的新上界,对任一顶点数为n,边数为m的简单图G,若其色数为k,则有ρ(G)+ρ(Gc)≤2n(n-1)-2m/k+2m/k1/2,其中k,m=12n(n-1)-m分别表示Gc的色数、边数。从而改进了已有的结果。

In this paper, the new upper bounds on sum of the spectral radius of graph and its complement are given. For any simple graph G with n vertices, m edges and chromatic number k, we have (ρ(G)+)ρ(G^c)≤2n(n-1)-2m/k+2/^(1/2), where and =12n(n-1)-m denote the chromatic number and edge number of G^c respectively. And this conclusion is better than the existing results.