On signed domination number of Cartesian product of directed paths
Abstract
In a digraph D = (V(D), A(D)), a two-valued function / : V(D) -> {-1,1} defined on the vertices of £> is called a signed dominating function if /(/Vlvl) > 1 for every v in D. The weight of a signed dominating function is f(V(D)) - The signed domination number ys(D) is the minimum weight among all signed dominating functions of D. Let P,n x Pn be the Cartesian product of directed paths Pm and Pn. Zhang and Shaheen [Z. Zhang and R. Shaheen, On signed domination number of Cartesian product of directed paths, Asian Journal of Mathematics and Computer Research, 18 (2017), 113-119| determined the exact value of 7i{Pm x Pn) for any 1 < m < 6 and n> 1. In this paper, the exact value of y5(Pm x P) is established for the remaining cases. © 2018 Utilitas Mathematica Publishing Incorporated. All rights reserved.
