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 -