On the revised Szeged index

We give bounds for the revised Szeged index, and determine the n-vertex unicyclic graphs with the smallest, the second-smallest and the third-smallest revised Szeged indices for n>=5, and the n-vertex unicyclic graphs with the kth-largest revised Szeged indices for all k up to 3 for n=5, to 5 for n=6, to 6 for n=7, to 7 for n=8, and to @?n2@?+4 for n>=9. We also determine the n-vertex unicyclic graphs of cycle length r, 3@?r@?n, with the smallest and the largest revised Szeged indices.

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