An inequality for degree sequences
The authors prove that \[ \left(\sum^ n_{i=1} d^{1/p}_ i\right)^ p\geq \sum^ n_{i=1} d^ p_ i \] for the degree sequence \(d_ 1,\dots,d_ n\) of a simple graph and \(p\) a positive integer. Moreover, they analyze also related ``real'' inequalities. Some partial results are interesting for their own sake, e.g. the authors present a generalization of Chebyshev's inequality and they sharpen the inequality of arithmetic and harmonic means (in some cases).
scientific article; zbMATH DE number 69892