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Abstract
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The non-commuting graph of a group 𝐺, denoted by ΓG, is a graph whose vertices are elements of 𝐺∖𝑍(𝐺) and two distinct vertices 𝑥 and y are adjacent if and only if 𝑥𝑦≠𝑦𝑥. In this paper, We classify groups whose domination number is one or two
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