Volume 16, Issue 2 (10-2021)
IJMSI 2021, 16(2): 1-10 |
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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
URL: http://ijmsi.ir/article-1-1138-en.html
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.
Keywords: Zero divisor graph, Domination number, Measurable function, Clique number, Coloring.
Type of Study: Research paper |
Subject:
General
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