Interval vertex coloring of cartesian products and strong products of paths

For the graph’s vertex coloring, it is required that for every vertex in a graph, the colors used in its open neighborhood or closed neighborhood must be able to form a continuous integer interval. A coloring is called an open neighborhood interval vertex coloring or a closed neighborhood interval vertex coloring of a graph if the neighborhood satisfying the condition is open or closed. In this paper, the interval vertex coloring of cartesian products and strong products of two paths is studied, and the low bound of the interval chromatic number is given.