On the sum of powers of the degrees of graphs

Authors

  • R. Xu
  • J. Wu
  • G. Wang
  • X. Zhang

Keywords:

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

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

Published

2013-09-27

Issue

Vol. 88 No. 3 (2013)

Section

Articles
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