@article{Article_26,

title = {Italian domination number upon vertex and edge removal},

journal = {Communications in Combinatorics, Cryptography & Computer Science},

volume = {2022},

issue = {1},

issn = { 2783-5456 },

year = {2022},

url = {http://cccs.sgh.ac.ir/Articles/2022/issue 1/1-2-Italiandominationnumberuponvertexandedgeremoval.pdf},

author = {S. Nazari-Moghaddam},

keywords = {Edge removal, Italian domination number, Italian dominating function, Graph, Vertex removal.},

abstract = {For a graph G = (V, E), italian domination function f : V -> {0, 1, 2} has the property that for every vertex v ∈ V with f(v) = 0, either v is adjacent to a vertex assigned 2 under f, or v is adjacent to at least two vertices assigned 1 under f. The weight of an italian domination function is the sum of its function values over all vertices. The italian domination number ɣ_I(G) equals the minimum weight of an italian dominating function on G. In this paper, we consider the effects of vertex and edge removal on the Italian domination number of a graph. In addition, we characterize the family of cartesian product of some graphs in terms of Italian domination number.}

};