Bagging Approach for Italian Domination in $C_{n} \square\,P_{m}$

Abstract

For graph G = (V, E), the open neighborhood of a vertex v is N(v) = {u ∈ V|uv ∈ E}. A function f : V (G) → {0, 1, 2} is called an Italian dominating function of G if Σ u∈N(v) f (u) ≥ 2, for each vertex f (v) = 0. The weight of f is w( f) = Σ v∈V(G) f (v). The minimum weight of an Italian dominating function of G is called the Italian domination number of G, denoted by y I (G). In this paper, we present a bagging approach and a partitioning approach to investigate the Italian domination number of Cartesian product of circles and paths, Cn□ P m . We determine the exact values of the Italian domination numbers of C n □ P 3 , C 3 □ P m . We also present some bounds on the Italian domination number of C n □ P m for n, m ≥ 4.