Bond incident degree indices of fixed-order unicyclic graphs

A connected graph with the same order and size is known as a unicyclic graph.For a vertex u in a graph, we denote its degree by du.For a unicyclic graph G of a given order, we investigate an extremal problem concerning the degree-based graph invariants of the form BID f (G) = vwE(G) f (dv, dw), where E(G) represents the edge set of G and f is a symmetric non-negative function that depends on the degrees of adjacent vertices of G.These graph invariants are known as bond incident degree indices.One of our results provides a partial solution to an open problem proposed by Ergoti and Doli in [MATCH Commun.