New Bounds For Degree Sequence Of Graphs

• Main Author: Akbar Jahanbani
• Format: Article
• Language: English
• Published: Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova 2019-09-01
• Series: Computer Science Journal of Moldova
• Subjects: Degree sequence of graph; Maximum degree; Minimum degree
• Online Access: http://www.math.md/files/csjm/v27-n2/v27-n2-(pp188-203).pdf

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}).