Laplacian Energies of Vertices

TL;DR

This paper introduces new vertex-specific Laplacian energy measures in graphs, explores their properties, and links them to various graph invariants, enhancing understanding of graph spectral characteristics.

Contribution

It defines Laplacian and Normalized Laplacian energies of vertices and establishes their fundamental properties and relationships with graph invariants.

Findings

Derived properties of vertex Laplacian energies

Connected vertex energies to spectral and geometric graph quantities

Provided theoretical insights into graph spectral analysis

Abstract

In this work, we define the Laplacian and Normalized Laplacian energies of vertices in a graph, we derive some of its properties and relate them to combinatorial, spectral and geometric quantities of the graph.