Glasnik Matematicki, Vol. 49, No. 1 (2014), 1-12.

THE EDGE WIENER INDEX OF SUSPENSIONS, BOTTLENECKS, AND THORNY GRAPHS

Yaser Alizadeh, Ali Iranmanesh, Tomislav Došlić and Mahdieh Azari

Department of Mathematics, Tarbiat Modares University, P. O. Box: 14115-137, Tehran, Iran
e-mail: iranmanesh@modares.ac.ir

Faculty of Civil Engineering, University of Zagreb, Kačićeva 26, 10000 Zagreb, Croatia
e-mail: doslic@grad.hr

Department of Mathematics, Kazerun Branch, Islamic Azad University, P. O. Box: 73135-168, Kazerun, Iran
e-mail: azari@kau.ac.ir

Abstract.   Let G be a simple connected graph. The distance between the edges g and f E(G) is defined as the distance between the corresponding vertices g and f in the line graph of G. The edge-Wiener index of G is defined as the sum of such distances between all pairs of edges of the graph. Let G₁+G₂ and G₁ο G₂ be the join and the corona of graphs G₁ and G₂, respectively. In this paper, we present explicit formulas for the edge-Wiener index for these graphs. Then we apply our results to compute the edge-Wiener index of suspensions, bottlenecks, and thorny graphs.

2010 Mathematics Subject Classification.   05C12, 05C76, 92E10.

Key words and phrases.   Distance, edge-Wiener index, join, corona.

DOI: 10.3336/gm.49.1.01

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