On the revised Szeged index

We give bounds for the revised Szeged index, and determine the nn-vertex unicyclic graphs with the smallest, the second-smallest and the third-smallest revised Szeged indices for n≥5n≥5, and the nn-vertex unicyclic graphs with the kkth-largest revised Szeged indices for all kk up to 3 for n=5n=5, to 5 for n=6n=6, to 6 for n=7n=7, to 7 for n=8n=8, and to ⌊n2⌋+4 for n≥9n≥9. We also determine the nn-vertex unicyclic graphs of cycle length rr, 3≤r≤n3≤r≤n, with the smallest and the largest revised Szeged indices.