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Degree-weighted Sombor indices of trees and unicyclic graphs: An extremal approach | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 22 اردیبهشت 1404 اصل مقاله (431.28 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30315.2413 | ||
| نویسندگان | ||
| Nasrin Dehgardi* 1؛ Tomislav Došlić2 | ||
| 1Department of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, Iran | ||
| 2University of Zagreb, Faculty of Civil Engineering, Zagreb, Croatia | ||
| چکیده | ||
| We consider two generalizations of the Sombor index, obtained by weighting the standard contribution $\sqrt{d_\Omega(\eta)^2+d_\Omega(\eta')^2}$ of an edge $\eta\eta'$ of a graph $\Omega$ by the sum and by the product of degrees of its end-vertices, respectively. The first generalization has been considered under the name of the elliptic Sombor index, while the second one seems to be new. We consider trees and unicyclic graphs on a given number of vertices $n$ with a given maximum degree $\Delta $ and characterize the graphs minimizing both generalizations over those classes of graphs. | ||
| کلیدواژه‌ها | ||
| Sombor index؛ degree-weighted Sombor index؛ elliptic Sombor index؛ trees؛ unicyclic graphs | ||
| مراجع | ||
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