A general modeling of some vertex-degree based topological indices in benzenoid systems and phenylenes ?
A graph invariant I(G) I ( G ) of a connected graph G=(V,E) G = ( V , E ) contributed by the weights of all edges is defined as I(G)=?cijxij I ( G ) = ? c i j x i j with the summation over all edges, cij c i j is the weight of edges connecting vertices of degree i i and j j , xij x i j is the number of edges of G G connecting vertices of degree i i and j j . It generalizes Randi? index, Zagreb index, sum-connectivity index, GA1 G A 1 index, ABC index etc. In this paper, we first give the expressions for computing this invariant I(G) I ( G ) of benzenoid systems and phenylenes, and a relation between this invariant of a phenylene and its corresponding hexagonal squeeze, and then determine the extremal values of I(G) I ( G ) and extremal graphs in catacondensed benzenoid systems and phenylenes, and a unified approach to the extremal values and extremal graphs of Randi? index, the general Randi? index, Zagreb index, sum-connectivity index, the general sum-connectivity index, GA1 G A 1 index and ABC index in benzenoid systems and phenylenes.
benzenoid system phenylene graph invariant extremal graph