Volume 16, Issue 2 (10-2021)                   IJMSI 2021, 16(2): 1-10 | Back to browse issues page

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Assari A, Rahimi M. On Beck's Coloring for Measurable Functions. IJMSI 2021; 16 (2) :1-10
URL: http://ijmsi.ir/article-1-1138-en.html

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.

Type of Study: Research paper | Subject: General

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