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A labeling \(f\) of the vertices of a graph \(G\) is said \(k\)-\emph{equitable} if each weight induced by \(f\) on the edges of \(G\) appears exactly \(k\) times. A graph \(G\) is said \emph{equitable} if for every proper divisor \(k\) of its size, the graph \(G\) has a \(k\)-equitable labeling.
A graph \(G\) is a corona graph if \(G\) is obtained from two graphs, \(G_1\) and \(G_2\), taking one copy of \(G_ 1\), which is supposed to have order \(p$, and \(p\) copies of \(G_2\), and then joining by an edge the \(k^{th}\) vertex of \(G_1\) to every vertex in the \(k^{th}\) copy of \(G_2\). We denote \(G\) by \(G_1 \otimes G_2\).
In this paper, we proved that the corona graph \(C_n \otimes K_1\) is equitable. Moreover, we show \(k\)-equitable labelings of the corona graph \(C_m \otimes nK_1\), for some values of the parameters \(k, m,\) and \(n\).