Dual Bandwidth of the product of two paths

AbstractThe dual bandwidth of a graph, is the maximum value of the minimum labeling variance of any two adjacent vertices. The computational complexity of finding the dual bandwidth of a general graph is Np-complete. Even the problem of deciding whether the dual bandwidth of graph is two or not is Np-complete. Therefore, we consider the dual bandwidth of special graphs- the product of two paths. We find the upper and lower bound of these graphs