A lower bound on the modified Randić index of line graphs

Abstract

The modified Randić index of a graph G is denoted by R′(G)=∑uv∈E(G)1maxd(u),d(v), where d(u) is the degree of vertex u. Wang et al. (2023), Zhang and Wu (2022) obtained the lower bounds of Randić index and harmonic index of the line graph of any tree of T with n≥3, i.e. R(L(T))>n4 and H(L(T))>n4. In this paper, we consider the modified Randić index of the line graph of any tree T with n≥3, which implies the results of Wang et al. (2023), Zhang and Wu (2022).