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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.

Notes on topological indices of graph and its complement

Madaras T., Mockovciakova M.

Opuscula Mathematica

2013

Vol. 33, no. 1

107-115

In this note, we derive the lower bound on the sum for Wiener index of bipartite graph and its bipartite complement, as well as the lower and upper bounds on this sum for the Randić index and Zagreb indices. We also discuss the quality of these bounds.