Applications of Generalized Hierarchical Product of Graphs in Computing the Szeged Index of Chemical Graphs

Let e be an edge of a graph G with endpoints u and v. Define two sets G1(e) and G2(e), G1(e) is the set of vertices closer to u than to v while G2(e) consists of those vertices that are closer to v. Then the Szeged index of G is defined as Sz(G )= � e∈E(G)(|G1(e)||G2(e)|). The generalized hierarchical product of graphs ⎧ ⎪ ⎪ ⎪ ⎪

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