Vertex-degree function index on tournaments

Document Type : Original paper

Authors

1 Department of Economy, Quantitative Methods and Economic History, Pablo de Olavide University, Carretera de Utrera Km. 1, 41013-Sevilla, Spain

2 Instituto de Matemáticas, Universidad de Antioquia, Medellín, Colombia

Abstract

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 $\left[ 0,+\infty \right)$.  

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References

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Communications in Combinatorics and Optimization
Volume 10, Issue 2
June 2025
Pages 443-452

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