Chebyshev's Sum Inequality and the Zagreb Indices Inequality
Abstract
In a recent article, Nadeem and Siddique used Chebyshev's sum inequality to establish the Zagreb indices inequality M1/n M2/m for undirected graphs in the case where the degree sequence (di) and the degree-sum sequence (Si) 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.
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