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Wiener index of strong product of graphs

Peterin I., Zigert-Pletersek P.

Opuscula Mathematica

2018

Vol. 38, no. 1

81--94

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.

On the independence number of some strong products of cycle-powers

Jurkiewicz M., Kubale M., Ocetkiewicz K.

Foundations of Computing and Decision Sciences

2015

Vol. 40, No. 2

133--141

In the paper we give some theoretical and computational results on the third strong power of cycle-powers, for example, we have found the independence numbers α((C210)⊠3) = 30 and α((C414)⊠3) = 14. A number of optimizations have been introduced to improve the running time of our exhaustive algorithm used to establish the independence number of the third strong power of cycle-powers. Moreover, our results establish new exact values and/or lower bounds on the Shannon capacity of noisy channels.