Extreme Values of the Sum of the Powers of Degrees

Shenggui Zhang
Department of Applied Mathematics, Northwestern Polytechnical
University, Shaanxi 710072, P. R. China


Abstract     Full Text  PDF

In this talk, we will present some results on characterizing the graphs with the extreme values of the sum of the powers of degrees. Two specific classes of graphs, namely, unicyclic and bicyclic graphs, with the rest three smallest and largest values of the sum of the powers of degrees are completely characterized. For bipartite graphs with given number of vertices and edges, we determine the smallest and largest sum of the squares of degrees. Some related problems are also discussed.