Exact Wiener Index of the Direct Product of a Path and a Wheel Graph

Abstract

The direct product is one of the most important methods to construct large-scale graphs using existing small-scale graphs, and the topological structure parameters of the constructed large-scale graphs can be derived from small-scale graphs. For a simple undirected graph G , its Wiener index W G is defined as the sum of the distances between all different unordered pairs of vertices in the graph. Path is one of the most common and useful graphs, and it is found in almost all virtual and real networks; wheel graph is a kind of graph with good properties and convenient construction. In this paper, the exact value of the Wiener index of the direct product of a path and a wheel graph is given, and the obtained Wiener index is only derived from the orders of the two factor graphs.