AU - Assari, A. AU - Rahimi, M. TI - On Beck's Coloring for Measurable Functions PT - JOURNAL ARTICLE TA - IJMSI JN - IJMSI VO - 16 VI - 2 IP - 2 4099 - http://ijmsi.ir/article-1-1138-en.html 4100 - http://ijmsi.ir/article-1-1138-en.pdf SO - IJMSI 2 ABĀ  - 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. CP - IRAN IN - LG - eng PB - IJMSI PG - 1 PT - Research paper YR - 2021