On domination number of Cartesian product of directed paths
Let gamma (G) denote the domination number of a digraph G and let P(m)square P(n) denote the Cartesian product of P(m) and P(n), the directed paths of length m and n. In this paper, we give a lower and upper bound for gamma(P(m)square P(n)). Furthermore, we obtain a necessary and sufficient condition for P(m)square P(n) to have efficient dominating set, and determine the exact values: gamma(P(2)square P(n)) = n, gamma(P(3)square P(n)) = n + inverted right perpendicularn/4inverted left perpendicular, gamma(P(4)square P(n)) = n+inverted right perpendicular2n/3inverted left perpendicular, gamma(P(5)square P(n)) = 2n+ 1 and gamma(P(6 square)P(n)) = 2n+ inverted right perpendicularn+2/3inverted left perpendicular.
domination number cartesian product directed path