in this paper, the weighted szeged indices of cartesian product and corona product of twoconnected graphs are obtained. using the results obtained here, the weighted szeged indices ofthe hypercube of dimension n, hamming graph, c4 nanotubes, nanotorus, grid, t− fold bristled,sunlet, fan, wheel, bottleneck graphs and some classes of bridge graphs are computed.

For simplicity we follow the rules: x, y, y1, y2, z, a will be arbitrary, f , g, h, h′, f1, f2 will denote functions, i will denote a natural number, X, Y , Z, V1, V2 will denote sets, P will denote a permutation of X, D, D1, D2, D3 will denote non-empty sets, d1 will denote an element of D1, d2 will denote an element of D2, and d3 will denote an element of D3. We now state a number of proposit...

Under suitable conditions of connectivity or non-bipartiteness, each of the three standard graph products (the Cartesian product, the direct product and the strong product) satisfies the unique prime factorization property, and there are polynomial algorithms to determine the prime factors. This is most easily proved for the Cartesian product. For the other products, current proofs involve a no...