Mamta Verma | Searcharxiv

arXiv2025

New improved lower bounds for Zagreb indices of graphs

This paper presents new lower bounds for the first general Zagreb index $Z_{\alpha}(G)$ involving two, three, and four arbitrary degrees of vertices of a simple graph $G$. For the special cases $\alpha = 2$ and $\alpha = -2$, the results give sharper bounds for the first Zagreb index $M_1(G)$ and the modified first Zagreb index ${}^{m}M_1(G)$, thereby improving several well-known inequalities in the literature. Furthermore, some applications of the derived bounds for $M_1(G)$ are demonstrated, establishing new bounds for the second Zagreb index, the spectral radius, Nordhaus-Gaddum type bounds, and their corresponding coindices.

math.CO↗

arXiv2025

Some central moments inequalities with applications

In this paper, we first derive an inequality involving central moments for n real numbers, which in turn provides an extension of Theorem 2.2 of Wolkowicz and Styan [18]. Furthermore, we present refinements of various inequalities obtained by Sharma et al. [12-15] involving central moments for the case of n distinct integers. Moreover, we provide applications of our results in matrix theory and the theory of polynomial equations.

math.FA↗