Convex Italian Domination in Graphs
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Let G be a connected graph. A function f : V(G) → {0,1,2} is a con vex Italian dominating function (or CvIDF) if for each v ∈ V(G) for which f(v) = 0, u∈N(v) f(u) ≥ 2 and the set of vertices v for which f(v)= 0 is convex. The minimum weight v∈V(G) f(v) of a CvIDF of G is the convex Italian domination number of G. In this paper, we initiate the study of convex Italian domination in graphs. We determine the convex Italian domination numbers of some graphs including complementary prisms and shadow graphs, and we give realization results involving convex Italian domination, convex Roman domination and convex 2-domination numbers.
Abstract
Let G be a connected graph. A function f : V(G) → {0,1,2} is a con vex Italian dominating function (or CvIDF) if for each v ∈ V(G) for which f(v) = 0, u∈N(v) f(u) ≥ 2 and the set of vertices v for which f(v)= 0 is convex. The minimum weight v∈V(G) f(v) of a CvIDF of G is the convex Italian domination number of G. In this paper, we initiate the study of convex Italian domination in graphs. We determine the convex Italian domination numbers of some graphs including complementary prisms and shadow graphs, and we give realization results involving convex Italian domination, convex Roman domination and convex 2-domination numbers.