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Outer Independent Double Italian Domination Of Some Graph Products, Rouhollah Jalaei, Doost Ali Mojdeh
Outer Independent Double Italian Domination Of Some Graph Products, Rouhollah Jalaei, Doost Ali Mojdeh
Theory and Applications of Graphs
An outer independent double Italian dominating function on a graph G is a function f:V(G) →{0,1,2,3} for which each vertex x ∈ V(G) with {f(x)∈ {0,1} then Σy ∈ N[x]f(y) ⩾ 3 and vertices assigned 0 under f are independent. The outer independent double Italian domination number γoidI(G) is the minimum weight of an outer independent double Italian dominating function of graph G. In this work, we present some contributions to the study of outer independent double Italian domination of three graph products. We characterize the Cartesian product, lexicographic product and direct product of custom …