Revised Szeged Index of Product Graphs
نویسنده
چکیده
The Szeged index of a graph G is defined as S z(G) = ∑ uv = e ∈ E(G) nu(e)nv(e), where nu(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) ( nu(e) + nG(e) 2 ) ( nv(e) + nG(e) 2 ) , where nG(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, C4 nanotubes and nanotorus are computed.
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