%0 Journal Article
%T Minimal graphs with respect to the multiplicative version of some vertex-degree-based topological indices
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Eliasi, Mehdi
%D 2024
%\ 05/05/2024
%V
%N
%P -
%! Minimal graphs with respect to the multiplicative version of some vertex-degree-based topological indices
%K Graph parameter, topological index, General sum connectivity index, multiplicative Zagreb indices, Sombor index
%K Forgotten index
%R 10.22108/toc.2024.139624.2119
%X 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.
%U https://toc.ui.ac.ir/article_28369_c115b9b1d4c244c0ab96e7ecd024a887.pdf