We study Beck-like coloring of measurable functions on a measure space $Omega$ taking values in a measurable semigroup $Delta$‎. ‎To any‎

‎measure space $Omega$ and any measurable semigroup $Delta$ we assign a graph (called a zero-divisor graph) whose vertices are labelled by‎

‎the classes of measurable functions defined on $Omega$ and having values in $Delta$‎, ‎with two vertices $f$ and $g$ adjacent if $f.g=0$ a.e.‎. ‎We show that‎, ‎if $Omega$ is atomic‎, ‎then not only the Beckchr('39')s conjecture holds but also the domination number coincide to the clique number and chromatic number as well‎. ‎We also determine some other graph properties of such a graph‎.