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

Document Type : Research Paper

Author

Department of Mathematics , Khansar Faculty, University of Isfahan, Isfahan, Iran

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.

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References

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Transactions on Combinatorics

Articles in Press, Corrected Proof
Available Online from 05 May 2024

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  • Receive Date: 28 October 2023
  • Revise Date: 08 April 2024
  • Accept Date: 24 April 2024
  • Published Online: 05 May 2024

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