RT - Journal Article T1 - On Beck's Coloring for Measurable Functions JF - IJMSI YR - 2021 JO - IJMSI VO - 16 IS - 2 UR - http://ijmsi.ir/article-1-1138-en.html SP - 1 EP - 10 K1 - Zero divisor graph‎ K1 - ‎Domination number‎ K1 - ‎Measurable function‎ K1 - ‎Clique number‎ K1 - ‎Coloring‎. AB - 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. LA eng UL http://ijmsi.ir/article-1-1138-en.html M3 10.52547/ijmsi.16.2.1 ER -