2024/06/05 by Gerardo Arizmendi, Arizmendi, Gerardo, Diego Huerta +1
Mathematics · Physics and Astronomy · #05C09 #05C50 #Combinatorics #Combinatorics (math.CO) #Complex Network Analysis Techniques #Computer science #FOS: Mathematics #Graph #Graph theory and applications #Index (typography) #Limits and Structures in Graph Theory #Mathematics #World Wide Web
paper · pdf · doi:10.48550/arxiv.2406.03561
openalex publication_date 2024/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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)≥ 2R(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)≥ 2R(G) and E(G)≥ 2μ(G) where μ(G) is the matching number. We give other inequalities as applications to this result.