Opuscula Math. 36, no. 1 (2016), 5-23
http://dx.doi.org/10.7494/OpMath.2016.36.1.5

Opuscula Mathematica

# Vertex-weighted Wiener polynomials of subdivision-related graphs

Mahdieh Azari
Ali Iranmanesh
Tomislav Došlić

Abstract. Singly and doubly vertex-weighted Wiener polynomials are generalizations of both vertex-weighted Wiener numbers and the ordinary Wiener polynomial. In this paper, we show how the vertex-weighted Wiener polynomials of a graph change with subdivision operators, and apply our results to obtain vertex-weighted Wiener numbers.

Keywords: vertex-weighted Wiener numbers, vertex-weighted Wiener polynomials, subdivision graphs.

Mathematics Subject Classification: 05C76, 05C12, 05C07.

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• Mahdieh Azari
• Department of Mathematics Kazerun Branch, Islamic Azad University, P.O. Box: 73135-168, Kazerun, Iran
• Ali Iranmanesh
• Tarbiat Modares University, Faculty of Mathematical Sciences, Department of Pure Mathematics, P.O. Box: 14115-137, Tehran, Iran
• Tomislav Došlić
• University of Zagreb, Faculty of Civil Engineering, Kaciceva 26, 10000 Zagreb, Croatia
• Communicated by Dalibor Fronček.
• Received: 2014-12-18.
• Revised: 2015-06-14.
• Accepted: 2015-06-16.
• Published online: 2015-09-19.

Cite this article as:
Mahdieh Azari, Ali Iranmanesh, Tomislav Došlić, Vertex-weighted Wiener polynomials of subdivision-related graphs, Opuscula Math. 36, no. 1 (2016), 5-23, http://dx.doi.org/10.7494/OpMath.2016.36.1.5

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