Total Edge Irregularity Strength of Hexagonal Networks

Abstract

Given a graph $G=(V,E)$, a labeling $\mathrm{\partial }:V\cup E\to \{1,2,\dots ,k\}$ is called an edge irregular total $k$-labeling if for every pair of distinct edges $uv$ and $xy$, $\mathrm{\partial }(u)+\mathrm{\partial }(uv)+\mathrm{\partial }(v)\ne \mathrm{\partial }(x)+\mathrm{\partial }(xy)+\mathrm{\partial }(y)$. The minimum $k$ for which $G$ has an edge irregular total $k$-labeling is called the total edge irregularity strength of $G$. In this paper, we examine the hexagonal network, which is a well-known interconnection network, and obtain its total edge irregularity strength.