Minimal graphs with respect to the multiplicative version of some vertex-degree-based topological indices

Eliasi, Mehdi

doi:10.22108/toc.2024.139624.2119

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	Minimal graphs with respect to the multiplicative version of some vertex-degree-based topological indices
Transactions on Combinatorics
مقاله 3، دوره 14، شماره 3، آذر 2025، صفحه 157-172 اصل مقاله (552.35 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2024.139624.2119
نویسنده
Mehdi Eliasi^*
Department of Mathematics , Khansar Faculty, University of Isfahan, Isfahan, Iran
چکیده
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.
کلیدواژه‌ها
Graph parameter, topological index, General sum connectivity index, multiplicative Zagreb indices, Sombor index؛ forgotten index

مراجع
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Minimal graphs with respect to the multiplicative version of some vertex-degree-based topological indices