@ARTICLE{Assari, author = {Assari, A. and Rahimi, M. and }, title = {On Beck's Coloring for Measurable Functions}, volume = {16}, number = {2}, abstract ={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. }, URL = {http://ijmsi.ir/article-1-1138-en.html}, eprint = {http://ijmsi.ir/article-1-1138-en.pdf}, journal = {Iranian Journal of Mathematical Sciences and Informatics}, doi = {10.52547/ijmsi.16.2.1}, year = {2021} }