On the sum of powers of the degrees of graphs

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


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}.



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

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