New Bounds For Degree Sequence Of Graphs

摘要

Let $G = (V, E)$ be a simple graph with $n$ vertices, $m$ edges, and vertex degrees $d_1, d_2, ..., d_n$. Let $d_1, d_n$ be the maximum and and minimum degree of vertices. In this paper, we present lower and upper bounds for $sum_{i=1}^{n}d_i^{2}$ and $sum_{i=1}^{n}d_i^{3}$ and relations between them. Also, we improve the bounds given in (ef{sor1}) and (ef{sor2}).