Abstract
An Italian dominating function (IDF) of a graph G is a function [Formula: see text] satisfying the condition that for every [Formula: see text] with [Formula: see text] The weight of an IDF on [Formula: see text] is the sum [Formula: see text] and Italian domination number, [Formula: see text] is the minimum weight of an IDF. In this paper, we prove that [Formula: see text] where [Formula: see text] is the Mycielskian graph of [Formula: see text]. We have also studied the impact of edge addition on Italian domination number. We also obtain a bound for the Italian domination number of Sierpinski graph [Formula: see text] and find the exact value of [Formula: see text].
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