On max-min rodeg index of graphs

Articles in Press

Document Type : Original paper

Authors

Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India

Abstract

Among the defined $148$ discrete Adriatic indices, the max-min rodeg index is one. It is a good predictor for the enthalpy of vaporization and standard enthalpy of vaporization for octane isomers, as well as the log water activity coefficient for polychlorobiphenyls.  For a graph $G$, here we concentrate on the max-min rodeg index, defined as
 \begin{equation*}
Mm_{sde}(G)=\sum_{x\sim y}\sqrt{\frac{max\{d_x, d_y\}}{min\{d_x, d_y\}}},
\end{equation*}
where $x\sim y$ and $d_x$ represents the adjacency of two vertices $x$ and $y$, and the degree of the vertex $x$, respectively. First, we present some bounds for the max-min rodeg index via standard inequalities. Then we provide upper bounds via some graph parameters for the max-min rodeg index of $G$. Also, we obtain a relation between the max-min degree index and the energy of $G$. Finally, we study the extremal value problem over chemical graphs concerning the max-min rodeg index.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 19 February 2026

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