Energy of a Vertex
Octavio Arizmendi, Jorge Fernandez Hidalgo, Oliver Juarez-Romero
TL;DR
This paper extends the concept of vertex energy in graphs, deriving inequalities, exploring properties, and generalizing the definition to locally finite graphs, contributing to spectral graph theory.
Contribution
It introduces an extended definition of vertex energy for locally finite graphs and establishes foundational inequalities and properties.
Findings
Derived basic inequalities for vertex energy
Explored continuity properties of vertex energy
Extended the concept to locally finite graphs
Abstract
In this paper we develop the concept of energy of a vertex introduced in Arizmendi and Juarez-Romero (2016). We derive basic inequalities, continuity properties, give examples and extend the definition to locally finite graphs.
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Limits and Structures in Graph Theory