The Edge Szeged Index of Product Graphs

The edge Szeged index of a molecular graph G is defined as the sum of products mu(e|G)mv(e|G) over all edges e = uv of G, where mu(e|G) is the number of edges whose distance to vertex u is smaller than the distance to vertex v, and where mv(e|G) is defined analogously. The aim of this paper is to compute the edge Szeged index of the Cartesian product of graphs. As a consequence of our result, the edge Szeged index of Hamming graphs and C4-nanotubes are computed.