Geodesic
The Wiener number of powers of the Mycielskian
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 3, pp. 489-498

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The Wiener number of a graph G is defined as 1/2 ∑_u,v ∈ V(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 μ(G) of graphs G. Using this, we show that for k ≥ 1, W(μ(Sₙ^k)) ≤ W(μ(Tₙ^k)) ≤ W(μ(Pₙ^k)), 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 μ(G^k).
Keywords: Wiener number, Mycielskian, powers of a graph 
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Balakrishnan, Rangaswami; Raj, S. The Wiener number of powers of the Mycielskian. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 3, pp. 489-498. http://geodesic.mathdoc.fr/item/DMGT_2010_30_3_a10/