Limit theorems for Randic index for Erd\H{o}s-Renyi graphs

TL;DR

This paper proves that the generalized Randic index for Erdős-Rényi graphs becomes highly concentrated around its average as the number of vertices grows large, in both sparse and dense regimes.

Contribution

It establishes the concentration behavior of the generalized Randic index for Erdős-Rényi graphs in all regimes, extending understanding of graph invariants.

Findings

Randic index concentrates around mean in large graphs

Results apply to both sparse and dense Erdős-Rényi regimes

Provides theoretical foundation for Randic index behavior in random graphs

Abstract

We prove that the generalized Randic index over graphs following the Erd\H{o}s-Renyi model, for both the sparse and dense regimes, is concentrated around its mean when the number of vertices tends to infinity.