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Vertex-degree function index on tournaments | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 23 آذر 1402 اصل مقاله (433.83 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28904.1771 | ||
| نویسندگان | ||
| Juan Rada* 1؛ Roberto Cruz1؛ Sergio Bermudo2 | ||
| 1Universidad de Antioquia | ||
| 2Department of Economy, Quantitative Methods and Economic History, Pablo de Olavide University, Carretera de Utrera Km. 1, 41013-Sevilla, Spain | ||
| چکیده | ||
| Let $G$ be a simple graph with vertex set $V=V(G)$ and edge set $E=E(G)$. For a real function $f$ defined on nonnegative real numbers, the vertex-degree function index $H_{f}(G)$ is defined as $$H_{f}(G)=\sum_{u\in V(G)}f(d_{u}).$$ In this paper we introduce the vertex-degree function index $H_{f}(D)$ of a digraph $D$. After giving some examples and basic properties of $H_{f}(D)$, we find the extremal values of $H_{f}$ among all tournaments with a fixed number of vertices, when $f$ is a continuous and convex (or concave) real function on $\left[ 0,+\infty \right)$. | ||
| کلیدواژه‌ها | ||
| Tournaments؛ Vertex-degree function index؛ Vertex-degree-based topological index | ||
| مراجع | ||
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[10] I. Tomescu, Extremal vertex-degree function index for trees and unicyclic graphs with given independence number, Discrete Appl. Math. 306 (2022), 83–88. https://doi.org/10.1016/j.dam.2021.09.028 [11] I. Tomescu, Graphs with given cyclomatic number extremal relatively to vertex degree function index for convex functions, MATCH Commun. Math. Comput. Chem. 87 (2022), no. 1, 109–114. | ||
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