Original Research Article

Article volume = 2022 and issue = 1

Pages: 7–10

Article publication Date: November 21, 2022

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# Italian domination number upon vertex and edge removal

#### S. Nazari-Moghaddam

Ilam University, Ilam, Iran.

##### 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<sub>I</sub>(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.

##### Keywords:

Edge removal, Italian domination number, Italian dominating function, Graph, Vertex removal.

##### References:

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##### Cite this article as:

- S. Nazari-Moghaddam, Italian domination number upon vertex and edge removal, Communications in Combinatorics, Cryptography & Computer Science, 2022(1), PP.7–10, 2022
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