Malaysian Journal of Mathematical Sciences, September 2024, Vol. 18, No. 3
Computing the Edge Irregularity Strength of Some Classes of Grid Graphs
Shahzad, M., Hasni, R., Tarawneh, I., and Asim, M. A.
Corresponding Email: [email protected]
Received date: 14 November 2023
Accepted date: 10 June 2024
Abstract:
Let $G$ be a simple graph. A function $\phi:V(G) \rightarrow \{1,2,\ldots, k\}$ a vertex $k$-labeling which assigns labels to the vertices of $G$. For any edge $xy$ in $G$, we define the weight of this edge as $w_{\phi}(xy) = \phi(x) + \phi(y)$. If all the edge weights are distinct, then $\phi$ is termed as an edge irregular $k$-labeling of $G$. The smallest possible value of $k$ for which the graph $G$ possesses an edge irregular $k$-labeling is denoted as the edge irregularity strength of $G$ and is represented as $es(G)$. In this paper, we investigate the edge irregular $k$-labeling of some classes of grid graphs, namely rhombic graph $R_{n}^m$, triangular graph $L_n^m$ and octagonal graph $O_n^m$. As by-product, we obtain their precise value of edge irregularity strength.
Keywords: rhombic grid; triangular grid; octagonal grid; edge irregular $k$-labeling; edge irregularity strength
