This article discusses the coloring of anti-fuzzy graph product. We studied the coloring of the anti-fuzzy graph direct product and came up with several properties. The coloring of anti-fuzzy graph direct product is a vertex coloring on the new anti-fuzzy graph obtained from the direct product of the anti-fuzzy graph whose vertices are colored. In general, the coloring of two anti-fuzzy graphs direct product with different of coloring each vertices is a coloring anti-fuzzy graph. The coloring of two strong anti-fuzzy graphs with different of coloring each vertices is a coloring strong anti-fuzzy graph. Other than that, different of coloring anti-fuzzy products are also discussed.

1.
M.
Akram
, “
Anti Fuzzy Structures on Graphs
,” in
Middle East Journal of Scientific Research,
pp.
1641
1648
(
2012
).
2.
R.
Muthuraj
and
A.
Sasireka
, “
Some Characterization on Operations of Anti Fuzzy Graphs
,” in
International Conference on Mathematical Impacts in Science And Technology, (MIST-17), IJRASET
, pp.
109
117
(
2017
).
3.
Y.
Trisanti
,
T.
Nusantara
,
A. B.
Gani
and
H.
Susanto
, “
Different types of product of anti fuzzy graph
,” in
The 2nd International Conference on Science, Mathematics, Environment, and Education,
AIP Conference Proceedings
, pp.
1
10
(
2019
).
4.
Y.
Trisanti
, “
Product Characteristics on Anti Fuzzy Graphs," Thesis
,
State University of Malang
, (
2019
).
5.
S.
Munoz
,
T.
Ortuno
,
J.
Ramirez
and
J.
Yanez
, “
Coloring Fuzzy Graphs
,” in
Omega,
pp.
211
221
(
2005
).
6.
C.
Eslachi
and
B. N.
Onagh
, “
Vertex Strenght of Fuzzy Graphs
,” in
International Journal of Mathematics and Mathematical Sciences,
(
2006
).
7.
M.A.
Rifayathali
,
A.
Prasanna
and
S. Ismail
Mohideen
, “
Chromatic Excellence in Anti Fuzzy Graphs
,” in
Journal of Applied Science and Computations,
pp.
305
316
(
2018
).
8.
R.
Seethalakshmi
and
R.B.
Gnanajothi
, “
Operations on Anti Fuzzy Graphs
,” in
Mathematical Sciences International Research Journal,
pp.
210
214
(
2016
).
9.
T.
Nusantara
,
D.
Rahmadani
,
M.
Hafiizh
and
E. D.
Cahyanti
, “
On Vertice and Edge Regular Anti Fuzzy Graphs
,” in
Journal of Physics,
Annual Conference on Science and Technology Research (ACOSTER
), (
2021
).
10.
R.
Muthuraj
and
A.
Sasireka
, “
Some Types of Nodal and Edge Regular Anti Fuzzy Graph
,” in
International Journal of Fuzzy Mathematical Archive,
pp.
365
378
(
2017
).
11.
R. M. a. A.
Sasireka
, “
Connected Domination
,” in
Journal of Applied Science and,
pp.
18
28
(
2018
).
12.
G.
Chartrand
and
P.
Zhang
,
Chromatic Graph Theory
(
CRC Press
,
A Chapman & Hall book
,
2009
).
13.
M.
Pal
,
S.
Samanta
and
G.
Ghorai
,
Modern Trends in Fuzzy Graph Theory
(
Springer
,
Singapore
,
2020
).
14.
R.
Muthuraj
and
A.
Sasireka
, “
Dominator Coloring on Anti Fuzzy Graph
,” in
Malaya Journal of Matematik,
pp.
217
223
(
2019
).
This content is only available via PDF.
You do not currently have access to this content.