Joins, coronas and their vertex-edge Wiener polynomials

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Published: Jun 30, 2016
DOI: https://doi.org/10.5556/j.tkjm.47.2016.1824
Keywords:
Distance Topological index Graph polynomial Graph operation

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Mahdieh Azari
Ali Iranmanesh

Abstract

The vertex-edge Wiener index of a simple connected graph $G$ is defined as the sum of distances between vertices and edges of $G$. The vertex-edge Wiener polynomial of $G$ is a generating function whose first derivative is a $q-$analog of the vertex-edge Wiener index. Two possible distances $D_1(u, e|G)$ and $D_2(u, e|G)$ between a vertex $u$ and an edge $e$ of $G$ can be considered and corresponding to them, the first and second vertex-edge Wiener indices of $G$, and the first and second vertex-edge Wiener polynomials of $G$ are introduced. In this paper, we study the behavior of these indices and polynomials under the join and corona product of graphs. Results are applied for some classes of graphs such as suspensions, bottlenecks, and thorny graphs.

Article Details

How to Cite
Azari, M., & Iranmanesh, A. (2016). Joins, coronas and their vertex-edge Wiener polynomials. Tamkang Journal of Mathematics, 47(2), 163–178. https://doi.org/10.5556/j.tkjm.47.2016.1824
Issue
Vol. 47 No. 2 (2016)
Section
Papers
Author Biographies

Mahdieh Azari

Department of Mathematics, Kazerun Branch, Islamic Azad University, P. O. Box: 73135-168, Kazerun, Iran.

Ali Iranmanesh

Department of PureMathematics, Faculty of Mathematical Sciences, TarbiatModaresUniversity, P. O. Box: 14115- 137, Tehran, Iran.

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