### On the sum of powers of the degrees of graphs

#### Abstract

For positive integers p and q, let G_{p,q} be a class of graphs such that |E(G)| ≤

p|V (G)| − q for every G ∈ G_{p,q}. In this paper, we consider the sum of the k-th powers

of the degrees of the vertices of a graph G ∈ G_{p,q}. Furthermore, we obtain bounds for

that sum of 1-planar graphs, t-degenerate graphs and series-parallel graphs, which are

all linear in ∆^{k−1}.

10.1017/S0004972713000063

p|V (G)| − q for every G ∈ G_{p,q}. In this paper, we consider the sum of the k-th powers

of the degrees of the vertices of a graph G ∈ G_{p,q}. Furthermore, we obtain bounds for

that sum of 1-planar graphs, t-degenerate graphs and series-parallel graphs, which are

all linear in ∆^{k−1}.

10.1017/S0004972713000063

#### Keywords

degree sum, 1-planar graph, series-parallel graph, degenerate graph

**Remember,**for most actions you have to record/upload into OJS

**and then**inform the editor/author via clicking on an email icon or Completion button.

Bulletin of the Aust. Math. Soc., copyright Australian Mathematical Publishing Association Inc.