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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