27 research outputs found
Outer Independent Double Italian Domination of Some Graph Products
An outer independent double Italian dominating function on a graph is a function for which each vertex with then and vertices assigned under are independent. The outer independent double Italian domination number is the minimum weight of an outer independent double Italian dominating function of graph . 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 graphs in terms of this parameter. We also provide the best possible upper and lower bounds for these three products for arbitrary graphs
Edge Italian Domination in some wheel related graphs
A function f:E(G) β{0,1,2} is an edge Italian dominating function (EIDF) if it satisfies the rule that every edge with weight 0 is either adjacent to an edge with weight 2 or adjacent to at least two edges with weight 1 each. The weight of an EIDF is β_(eβE(G))βγf(e)γ. The minimum β_(eβE(G))βγf(e)γis the edge Italian domination number (EIDN). The symbol (Ξ³_I ) Μ (G) is used to denote the EIDN. In this paper, we obtain the EIDN of some wheel related graphs like gear graph, helm graph, flower graph, web graph etc
The Italian domination numbers of some products of directed cycles
An Italian dominating function on a digraph with vertex set is
defined as a function such that every vertex
with has at least two in-neighbors assigned under
or one in-neighbor with . In this paper, we determine the
exact values of the Italian domination numbers of some products of directed
cycles