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Edge-Wiener Indices of Composite Graphs

  • Mahdieh Azari
  • Ali IranmaneshEmail author
Chapter
Part of the Carbon Materials: Chemistry and Physics book series (CMCP, volume 9)

Abstract

The distance d(u, v|G) between the vertices u and v of a simple connected graph G is the length of any shortest path in G connecting u and v. The Wiener index W(G) of G is defined as the sum of distances between all pairs of vertices of G. The edge-Wiener index of G is conceived in an analogous manner as the sum of distances between all pairs of edges of G. Two possible distances d 0(e, f|G) and d 4(e, f|G) between the edges e and f of G can be considered and according to them, the corresponding edge-Wiener indices \( {W}_{e_0}(G) \) and \( {W}_{e_4}(G) \) are defined. In this chapter, we report our recent results on computing the first and second edge-Wiener indices of some composite graphs. Results are illustrated by some interesting examples.

Keywords

Distance Edge-Wiener indices Edge-Wiener polynomials Composite graphs 

Notes

Acknowledgment

Partial support by the Center of Excellence of Algebraic Hyper-structures and its Applications of Tarbiat Modares University (CEAHA) is gratefully acknowledged by the second author (AI).

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Kazerun BranchIslamic Azad UniversityKazerunIran
  2. 2.Department of Pure Mathematics, Faculty of Mathematical SciencesTarbiat Modares UniversityTehranIran

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