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Coloring in essential annihilating-ideal graphs of commutative rings
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Journal Article
Coloring in essential annihilating-ideal graphs of commutative rings
2024
Overview
The essential annihilating-ideal graph
E
G
(
R
)
of a commutative unital ring
R
is a simple graph, whose vertices are non-zero ideals of
R
with non-zero annihilator and there exists an edge between two distinct vertices
I
,
J
if and only if
Ann
(
IJ
) has a non-zero intersection with any non-zero ideal of
R
. In this paper, we show that
E
G
(
R
)
is weakly perfect, if
R
is Noetherian and an explicit formula for the clique number of
E
G
(
R
)
is given. Moreover, the structures of all rings whose essential annihilating-ideal graphs have chromatic number 2 are fully determined. Among other results, twin-free clique number and edge chromatic number of
E
G
(
R
)
are examined.
Publisher
Springer Berlin Heidelberg
