Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2026 02 19 On max-min rodeg index of graphs 15115 10.22049/cco.2026.30730.2597 EN Biswaranjan Khanra Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India Shibsankar Das Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India 0000-0003-0082-6673 Journal Article 2025 06 21 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<br /> \begin{equation*}<br />Mm_{sde}(G)=\sum_{x\sim y}\sqrt{\frac{max\{d_x, d_y\}}{min\{d_x, d_y\}}},<br />\end{equation*}<br />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. https://comb-opt.azaruniv.ac.ir/article_15115_1fcebd7bb678e6d9d0557bd60c5f45e2.pdf