@article {
author = {Eliasi, Mehdi},
title = {Minimal graphs with respect to the multiplicative version of some vertex-degree-based topological indices},
journal = {Transactions on Combinatorics},
volume = {},
number = {},
pages = {-},
year = {2024},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2024.139624.2119},
abstract = {As a real-valued function, a graphical parameter is defined on the class of finite simple graphs, and remains invariant under graph isomorphism. In mathematical chemistry, vertex-degree-based topological indices are the graph parameters of the general form of $p_{\phi}(G)=\sum_{uv\in E(G)}\phi(d(u),d(v))$, where $\phi$ represents a real-valued symmetric function, and $d(u)$ shows the degree of $u\in V(G)$. In this paper, it is proved that if $\phi$ has certain conditions, then the graph among those with $n$ vertices and $m$ edges, whose difference between the maximum and minimum degrees is at most $1$, has the minimal value of $p_{\phi}$. Moreover, it is demonstrated that some well-known topological indices are able to satisfy these certain conditions, and the given indices can be treated in a unified manner.},
keywords = {Graph parameter, topological index, General sum connectivity index, multiplicative Zagreb indices, Sombor index,Forgotten index},
url = {https://toc.ui.ac.ir/article_28369.html},
eprint = {https://toc.ui.ac.ir/article_28369_c115b9b1d4c244c0ab96e7ecd024a887.pdf}
}