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 Hf(G) is defined as Hf(G)=uV(G)f(du). In this paper we introduce the vertex-degree function index Hf(D) of a digraph D. After giving some examples and basic properties of Hf(D), we find the extremal values of Hf among all tournaments with a fixed number of vertices, when f is a continuous and convex (or concave) real function on [0,+).  

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