Bounds on Fractional Domination of Some Products of Graphs

Let γf(G) and γtf(G) be the fractional domination number and fractional total domination number of a graph G respectively. Hare and Stewart gave some exact fractional domination number of Pn×Pm (grid graph) with small n and m. But for large n and m, it is difficult to decide the exact fractional domination number. Motivated by this, nearly sharp upper and lower bounds are given to the fractional domination number of grid graphs. Furthermore, upper and lower bounds on the fractional total domination number of strong direct product of graphs are given.