Abstract
A connected graph in which no edge lies on more than one cycle is called a cactus graph (also known as Husimi tree). A bond incident degree (BID) index of a graph G is defined as Sigma uv is an element of E is the edge set of G, and f is a real-valued symmetric function. This study involves extremal results of cactus graphs concerning the following type of the BID indices: Ifi, f1 is a strictly convex function, and f2 is a strictly concave function. More precisely, graphs attaining the minimum and maximum Ifi values are studied in the class of all cactus graphs with a given number of vertices and cycles. The obtained results cover several well-known indices including the general zeroth-order Randi index, multiplicative first and second Zagreb indices, and variable sum exdeg index.