TY - JOUR
T1 - On Beck's Coloring for Measurable Functions
TT -
JF - IJMSI
JO - IJMSI
VL - 16
IS - 2
UR - http://ijmsi.ir/article-1-1138-en.html
Y1 - 2021
SP - 1
EP - 10
KW - Zero divisor graph
KW - Domination number
KW - Measurable function
KW - Clique number
KW - Coloring.
N2 - 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.
M3 10.52547/ijmsi.16.2.1
ER -