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On max-min rodeg index of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 30 بهمن 1404 اصل مقاله (409.8 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30730.2597 | ||
| نویسندگان | ||
| Biswaranjan Khanra؛ Shibsankar Das* | ||
| Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| max-min rodeg index؛ Diaz-metcalf inequality؛ clique number؛ energy؛ chemical graph | ||
| مراجع | ||
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