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On extremal trees for the minimum Sombor index with fixed total domination number | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 آبان 1404 اصل مقاله (450.83 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30519.2511 | ||
| نویسندگان | ||
| S. Bermudo* 1؛ Paulo Guzmán2؛ Fateme Movahedi3 | ||
| 1Department of Economy, Quantitative Methods and Economic History, Pablo de Olavide University, Carretera de Utrera Km. 1, 41013-Sevilla, Spain | ||
| 2Facultad de Ciencias Agrarias, Universidad Nacional del Nordeste, Juan Bautista Cabral 2131, Corrientes, Argentina | ||
| 3Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran | ||
| چکیده | ||
| The Sombor index of a graph $G$ is a degree-based graph structure descriptor, defined as $SO(G)=\sum_{uv \in E(G)}\sqrt{d(u)^2+d(v)^2},$ in which $d(x)$ is the degree of the vertex $x \in V(G)$, for $x=u, v$. In this paper, we find a sharp lower bound of the Sombor index in trees with fixed total domination number and we characterize the extremal trees. More precisely, given any tree $T$ with order $n$ and total domination number $\gamma_t$, we prove that $SO(T)\geq \left(2\sqrt{13}+\sqrt{5}-\frac{7\sqrt{2}}{2}\right)(n-2\gamma_t)+4\sqrt{2}\gamma_t+2\sqrt{5}-6\sqrt{2}.$ This lower bound improves, in many cases, the known lower bounds given with the order and with the order and the domination number of the tree. | ||
تازه های تحقیق | ||
á | ||
| کلیدواژه‌ها | ||
| Sombor index؛ total domination number؛ tree | ||
| مراجع | ||
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