New Bounds For Degree Sequence Of Graphs

Abstract

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 (\ref{sor1}) and (\ref{sor2}).

Keywords

• Degree sequence of graph
• Maximum degree
• Minimum degree