Edge Italian Domination in Some Wheel Related Graphs
DOI:
https://doi.org/10.12723/mjs.sp1.6Keywords:
Italian Domination, Edge Italian Dominating function, Edge Italian domination numberAbstract
A function f:E(G) →{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 ∑_(e∈E(G))▒〖f(e)〗. The minimum ∑_(e∈E(G))▒〖f(e)〗is the edge Italian domination number (EIDN). The symbol (γ_I ) ́ (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.
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