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The proper divisor graph $\Upsilon_n$ of a positive integer $n$ is the simplegraph whose vertices are the proper divisors of $n$, and in which two distinctvertices $u, v$ are adjacent if and only if $n$ divides $uv$. The graph$\Upsilon_n$ plays an important role in the study of the zero divisor graph ofthe ring $\mathbb{Z}_n$. In this paper, we study some graph theoreticproperties of $\Upsilon_n$ and determine the graph parameters such as cliquenumber, chromatic number, chromatic index, independence number, matchingnumber, domination number, vertex and edge covering numbers of $\Upsilon_n$. Wealso determine the automorphism group of $\Upsilon_n$.

Proper divisor graph of a positive integer