The Edge Szeged Index of Product Graphs

By M. Khalifeh, H. Yousefi-Azari, Ali Reza Ashrafi, Ivan Gutmanc. 2008

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The edge Szeged index of a molecular graph G is defined as the sum of products m u (e|G)m v (e| G) over all edges e = uv of G, where m u (e|G) is the number of edges whose distance to vertex u is smaller than the distance to vertex v, and where m v (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 C 4 -nanotubes are computed.

View Paper: https://www.semanticscholar.org/paper/bdec68876eec0b03a679ca6edc292b1a3a62c1d5