Revised Szeged Index of Product Graphs

The Szeged index of a graph G is defined as S z(G) = ∑/uv=e∈E(G) n sub u /sub (e)n sub v /sub (e) where, n sub u /sub (e) is number of vertices of G whose distance to the vertex u is less than the distance to the vertex v in G Similarly, the revised Szeged index of G is defined . as S z*(G) = ∑/uv=e∈E(G) (n sub u /sub (e) + n sub G /sub (e)/2) (n sub v /sub (e) + n sub G /sub (e)/2), where n sub G /sub (e) is the number of equidistant vertices of e in G In this paper, the revised Szeged index of Cartesian . product of two connected graphs is obtained. Using this formula, the revised Szeged indices of the hypercube of dimension n Hamming graph, grid, C sub 4 /sub nanotubes and nanotorus are computed.