SZEGED INDEX OF A CLASS OF UNICYCLIC GRAPHS

The Szeged index is a modification of the Wiener index to cyclic molecules. The Szeged index of a connected graph G is defined as Sz(G) = Sigma(e is an element of E(G))n(1)(e vertical bar G)n(2)(e vertical bar G), where E(G) is the edge set of G, and for any e = u nu is an element of E(G), n(1)(e vertical bar G) is the number of vertices of G lying closer to vertex u than to vertex nu, and n(2)(e vertical bar G) is the number of vertices of G lying closer to vertex v than to vertex u. In this paper, we determine the n-vertex unicyclic graphs whose vertices on the unique cycle have degree at least three with the first, the second and the third smallest as well as largest Szeged indices for n >= 6, n >= 7 and n >= 8, respectively.