A graph invariant I(G) of a connected graph G=(V,E) contributed by the weights of all edges is defined as I(G)=∑ cij xij with the summation over all edges, Cij is the weight of edges connecting vertices of degree i and j, xij is the number of edges of G connecting vertices of degree i and j. It generalizes Randi index, Zagreb index, sum-connectivity index, GA1 index, ABC index etc. In this paper, we first give the expressions for computing this invariant I(G) of benzenoid systems and phenylenes, and a relation between this invariant of a pheny...
