English

Chebyshev's Sum Inequality and the Zagreb Indices Inequality

Combinatorics 2023-01-02 v1

Abstract

In a recent article, Nadeem and Siddique used Chebyshev's sum inequality to establish the Zagreb indices inequality M1/nM2/mM_1/n\le M_2/m for undirected graphs in the case where the degree sequence (di)(d_i) and the degree-sum sequence (Si)(S_i) are similarly ordered. We show that this is actually not a completely new result and we discuss several related results that also cover similar inequalities for directed graphs, as well as sum-symmetric matrices and Eulerian directed graphs.

Keywords

Cite

@article{arxiv.2212.14481,
  title  = {Chebyshev's Sum Inequality and the Zagreb Indices Inequality},
  author = {Hanjo Täubig},
  journal= {arXiv preprint arXiv:2212.14481},
  year   = {2023}
}