DOI: 10.18178/wcse.2018.06.059

## The Wiener Entropy And Average Distance Of Convex Honeycomb Mesh

*Xueli Su, Haizhen Ren, Shumin Zhang*

*Abstract*— Honeycomb mesh was first put forward by Stojmenovic in 1997. Honeycomb mesh with smaller diameter and degrees of nodes (vertices), is superior to other networks, so has a great application prospect. The Wiener number is a topological index defined as the sum of distance of all pairs of vertices in the graph, which was introduced in 1947 by Harold Wiener as the path number, it is one of the most widely studied topological indices. In addition, the Wiener index is also related to a parameter of the computer network, the average distance. The convex honeycomb mesh can be depicted by a piece of an Archimedean tiling (6.6.6) that is a partial cube. Inspired by this fact, the analytical expressions for Wiener numbers of three convex honeycomb meshes and their Wiener entropies are obtained. Furthermore, their asymptotic behaviors and average distances are also discussed.

*Index Terms*— partial cube, convex honeycomb mesh, Wiener number, entropy

Xueli Su, Haizhen Ren, Shumin Zhang

Department of Mathematics, Qinghai Normal University, CHINA

Cite: Xueli Su, Haizhen Ren, Shumin Zhang, "The Wiener Entropy And Average Distance Of Convex Honeycomb Mesh," *Proceedings of 2018 the 8th International Workshop on Computer Science and Engineering, pp. 330-334, Bangkok, 28-30 June, 2018.*