Closed graph property and Khalimsky spaces

In the following text for Khalimsky $n-$dimensional space ${\mathcal{K}}^n$ we show self–map $f:{\mathcal{K}}^n\to {\mathcal{K}}^n$ has closed graph if and only if there exist integers ${\lambda }_1,\dots ,{\lambda }_n$ such that $f$ is a constant map with value $(2{\lambda }_1,\cdots ,2{\lambda }_n)$. We also show each self–map on Khalimsky circle and Khalimsky sphere which has closed graph is a constant map. The text is motivated by examples.