Opuscula Math. 38, no. 1 (2018), 81-94
https://doi.org/10.7494/OpMath.2018.38.1.81

Opuscula Mathematica

# Wiener index of strong product of graphs

Iztok Peterin
Petra Žigert Pleteršek

Abstract. The Wiener index of a connected graph $$G$$ is the sum of distances between all pairs of vertices of $$G$$. The strong product is one of the four most investigated graph products. In this paper the general formula for the Wiener index of the strong product of connected graphs is given. The formula can be simplified if both factors are graphs with the constant eccentricity. Consequently, closed formulas for the Wiener index of the strong product of a connected graph $$G$$ of constant eccentricity with a cycle are derived.

Keywords: Wiener index, graph product, strong product.

Mathematics Subject Classification: 05C12, 05C76.

Full text (pdf)

• Iztok Peterin
• University of Maribor, Faculty of Electrical Engineering and Computer Science, Koroška 46, 2000 Maribor, Slovenia
• Institute of Mathematics, Physics, and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
• Petra Žigert Pleteršek
• University of Maribor, Faculty of Chemistry and Chemical Engineering, Smetanova 17, 2000 Maribor, Slovenia
• Institute of Mathematics, Physics, and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
• Communicated by Mirko Horňák.
• Revised: 2017-05-04.
• Accepted: 2017-05-04.
• Published online: 2017-11-13.