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Sharp upper bounds on $KG$-Sombor index of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 دی 1404 اصل مقاله (390.4 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31014.2709 | ||
| نویسندگان | ||
| Enkhbayar Azjargal؛ Batmend Horoldagva* ؛ Lkhagva Buyantogtokh؛ Shiikhar Dorjsembe | ||
| Department of Mathematics, Mongolian National University of Education, Baga toiruu-14, Ulaanbaatar, Mongolia | ||
| چکیده | ||
| The $KG$-Sombor index of a graph $G$ is defined as $$KG(G)=\sum_{\substack{u \in V(G) \\ e \in E(G) \\ u \sim e}}\sqrt{d_{G}^{2}(u)+d_{G}^{2}(e)},$$ where the summation goes over pairs of vertices $u$ and edges $e$ such that $e$ is incident to $u$. In this paper, we establish sharp upper bounds for the $KG$-Sombor index in three classes of graphs: graphs of order $n$ with $k$ pendent vertices, graphs of order $n$ with $k$ cut edges, and unicyclic graphs of order $n$ with girth $g$. Moreover, in each case, the extremal graphs attaining these bounds are completely characterized. | ||
| کلیدواژهها | ||
| Sombor index؛ KG-Sombor index؛ cut edge؛ pendent vertex | ||
| مراجع | ||
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