Abstract
A bond incident degree (BID) index of a graph G is defined as Sigma f(d(G)(u), d(G)(v)), with summation ranging over all pairs of adjacent vertices u, v of G, where d(G)(w) denotes the degree of the vertex w of G, and f is a real-valued symmetric function. This paper reports extremal results for BID indices of the type If(i) (G) = Sigma[f(i)(dG(u))/d(G)(u) + f(i)(dG(v))/d(G)(v)], where i is an element of {1, 2}, f(1) is strictly convex, and f(2) is strictly concave. Graphs attaining minimum If1 and maximum If2 are characterized from the class of connected (n, m)-graphs and chemical (n, m)-graphs, where n and m satisfy the conditions 3n >= 2m, n >= 4, m >= n+ 1. By this, we extend and complement the recent result by Tomescu [ MATCH Commun. Math. Comput. Chem. 85 (2021) 285-294], and cover several well-known indices, including general zeroth-order Randi ' c index, multiplicative first and second Zagreb indices, variable sum exdeg index, and Lanzhou index.