Work

Energy of a graph and Randić index of subgraphs

Year: 2025

Type: article

Abstract: We give a new inequality between the energy of a graph and a weighted sum over the edges of the graph. Using this inequality we prove that E ( G ) ≥ 2 R ( H ) , where E ( G ) is the energy of a graph G and R ( H ) is the Randić index of any subgraph of G (not necessarily induced). In particular, this generalizes well-known inequalities E ( G ) ≥ 2 R ( G ) and E ( G ) ≥ 2 μ ( G ) where μ ( G ) is the matching number. We give other inequalities as applications to this result.

Source: Discrete Applied Mathematics

DOI: 10.1016/j.dam.2025.04.029

Authors: Gerardo Arizmendi, Diego Huerta

Institution: Universidad de las Américas Puebla

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Consejo Nacional de Ciencia y Tecnología