The Edge-Wiener Index and Its Computation for Some Nanostructures
The first and the second edge versions of Wiener index, which were based on the distance between two edges in a connected graph G, were introduced by Iranmanesh et al. in (MATCH Commun Math Comput Chem 61:663, 2009).
In this chapter, at first we obtain the explicit relation between different versions of Wiener number and due to this relation, the edge-Wiener numbers of some graph have been computed. Then we find the first edge-Wiener index of the composition and sum of graphs. As an application of our results, we find the first and the second edge-Wiener indices of some nanostructures.
KeywordsConnected Graph Topological Index Wiener Index Black Vertex White Vertex
This work was partially supported by Center of Excellence of Algebraic Hyperstructures and its Applications of Tarbiat Modares University (CEAHA).
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