The Wiener number of powers of the Mycielskian

The Wiener number of a graph G is dened as 1 P u;v2V (G) d(u; v), d the distance function on G. The Wiener number has important applications in chemistry. We determine a formula for the Wiener number of an important graph family, namely, the Mycielskians (G) of graphs G. Using this, we show that for k 1, W ( (S k n)) W ( (T k n)) W ( (P k n )), where Sn, Tn and Pn denote a star, a general tree and a path on n vertices respectively. We also obtain Nordhaus-Gaddum type inequality for the Wiener number of (G k ).