Computing the edge irregularity strength of the strong product of two paths using an algorithmic approach

In this article, edge irregular labeling for the strong product of two paths e s ( P m ⊠ P n ) is computed algorithmically. The product of two paths P m and P n may form either a square or a rectangular graph. So, to cover all the possibilities of square and rectangular graphs an experiment is conducted by varying the values of m and n . To yield optimum labeling, algorithms are executed on computers with two different graph traversing techniques. These traversing techniques are named as the row-method and the matrix-method based on their working in one dimension and two dimensions respectively. Eventually the matrix-method resulted in the optimum labels and is considered the main outcome of this study. For the sake of a mathematical solution an upper-bound is suggested as ⌊ (V+E) 2 ⌋ using curve-based analysis. The algorithms designed in this study can be customized for similar graph families or for other types of labeling as well in the future.