The concept of domination in graphs is very ancient. Several types of notions of domination in graphs have been discussed by many researchers. In this work, the concept of domination and some notions of domination sets, minimal dominating sets, independence sets, and maximal independence sets are introduced in bipolar fuzzy soft graphs. Additionally, several properties of dominating sets are discussed and some theorems in bipolar fuzzy soft graphs are proved.
TutteW.T., Graph theory (Vol. 21). Cambridge university press, 2001.
2.
ZadehL.A., Fuzzy sets, Information and Control8(3) (1965), 338–353.
3.
RosenfeldA., Fuzzy graphs, In Fuzzy sets and their applications to cognitive and decision processes (pp. 77–95). Academic press, (1975).
4.
BhattacharyaP., Some remarks on fuzzy graphs, Pattern Recognition Letters6(5) (1987), 297–302.
5.
MordesonJ.N., NairP.S., MordesonJ.N. and NairP.S., Fuzzy graphs, Fuzzy Mathematics: An Introduction for Engineers and Scientists (2001), 21–65.
6.
AkramM., Bipolar fuzzy graphs with applications, Knowledge-Based Systems39 (2013), 1–8.
7.
AkramM., Interval-valued fuzzy line graphs, Neural Computing and Applications21 (2012), 145–150.
8.
AkramM. and DavvazB., Strong intuitionistic fuzzy graphs, Filomat26(1) (2012), 177–196.
9.
AkramM., Interval-valued fuzzy line graphs, Neural Computing and Applications21 (2012), 145–150.
10.
ZhangW.R. and ZhangL., YinYang bipolar logic and bipolar fuzzy logic, Information Sciences165(3-4) (2004), 265–287.
11.
ZadehL.A., Fuzzy sets, Information and Control8(3) (1965), 338–353.
12.
AkramM., Bipolar fuzzy graphs with applications, Knowledge-Based Systems39 (2013), 1–8.
13.
AkramM., Bipolar fuzzy graphs with applications, Knowledge-Based Systems39 (2013), 1–8.
14.
AkramM. and KarunambigaiM.G., Metric in bipolar fuzzy graphs, World Applied Sciences Journal14(12) (2011), 1920–1927.
15.
FengF., LiuX., Leoreanu-FoteaV. and JunY.B., Soft sets and soft rough sets, Information Sciences181(6) (2011), 1125–1137.
16.
FengF., JunY.B., LiuX. and LiL., An adjustable approach to fuzzy soft set based decision making, Journal of Computational and Applied Mathematics234(1) (2010), 10–20.
17.
FengF., LiC., DavvazB. and AliM.I., Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing14 (2010), 899–911.
18.
JiangY., TangY., ChenQ., WangJ. and TangS., Extending soft sets with description logics, Computers & Mathematics with Applications59(6) (2010), 2087–2096.
19.
GongK., XiaoZ. and ZhangX., The bijective soft set with its operations, Computers & Mathematics with Applications60(8) (2010), 2270–2278.
20.
NazM. and ShabirM., On fuzzy bipolar soft sets, their algebraic structures and applications, Journal of Intelligent & Fuzzy Systems26(4) (2014), 1645–1656.
21.
AbdullahS., AslamM. and UllahK., Bipolar fuzzy soft sets and its applications in decision making problem, Journal of Intelligent & Fuzzy Systems27(2) (2014), 729–742.
22.
CelikY.I.L.D.I.R.A.Y., On bipolar fuzzy soft graphs, Creative Mathematics and Informatics27(2) (2018), 123–132.
23.
Aygünoglu A. and AygünH., Introduction to fuzzy softgroups, Introduction to fuzzy soft groups, Computers & Mathematics with Applications58(6) (2009), 1279–1286.
24.
AkramM. and NawazS., On fuzzy soft graphs, Italian Journal of Pure and Applied Mathematics34 (2015), 497–514.
25.
AkramM., FengF., Borumand Saeid A. and Leoreanu-FoteaV., A new multiple criteria decision-making method based on bipolar fuzzy soft graphs, Iranian Journal of Fuzzy Systems15(4) (2018), 73–92.
26.
AminF., FahmiA. and AslamM., Approaches to multiple attribute group decision making based on triangular cubic linguistic uncertain fuzzy aggregation operators, Soft Computing24 (2020), 11511–11533.
27.
PalM., SamantaS., GhoraiG., Modern trends in fuzzy graph theory (pp. 7–93). Berlin: Springer, 2020.
28.
BergeC., Graphs and Hypergraphs, volume 6 of, (1973).
29.
CockayneE.J. and HedetniemiS.T., Towards a theory of domination in graphs, Networks7(3) (1977), 247–261.
30.
CockayneE.J., DawesR.M. and HedetniemiS.T., Total domination in graphs, Networks10(3) (1980), 211–219.
31.
ManjushaO.T., Set Domination in Fuzzy Graphs Using Strong Arcs, Pan-American Journal of Mathematics1 (2022), 9.
32.
ManjushaO.T. and SunithaM.S., Strong domination in fuzzy graphs, Fuzzy Information and Engineering7(3) (2015), 369–377.
33.
MerouaneH.B. and ChellaliM., On secure domination in graphs, Information Processing Letters115(10) (2015), 786–790.
34.
ArasC.G., Al-shamiT.M., MhemdiA., BayramovS., Local compactness and paracompactness on bipolar soft topological spaces, Journal of Intelligent & Fuzzy Systems (Preprint) (2022), 1–9.
35.
MalikN., ShabirM., Al-shamiT.M., GulR., ArarM., HosnyM., Rough bipolar fuzzy ideals in semigroups, Complex & Intelligent Systems (2023), 1–16.
36.
MalikN., ShabirM., Al-shamiT.M., GulR. and MhemdiA., Medical decision-making techniques based on bipolar soft information, AIMS Mathematics8(8) (2023), 18185–18205.
37.
GulR., ShabirM., Al-shamiT.M. and HosnyM., A Comprehensive study on (α, β)-multi-granulation bipolar fuzzy rough sets under bipolar fuzzy preference relation, AIMS Mathematics8(11) (2023), 25888–25921.
38.
Al-ShamiT.M., Bipolar soft sets: relations between them and ordinary points and their applications, Complexity2021 (2021), 1–14.
39.
ShabirM. and GulR., Modified rough bipolar soft sets, Journal of Intelligent & Fuzzy Systems39(3) (2020), 4259–4283.
40.
GulR., ShabirM., MashwaniW.K. and UllahH., Novel Bipolar Soft Rough-Set Approximations and Their Application in Solving Decision-Making Problems, International Journal of Fuzzy Logic and Intelligent Systems22(3) (2022), 303–324.
41.
GulR., ShabirM., NazM. and AslamM., A novel approach toward roughness of bipolar soft sets and their applications in MCGDM, IEEE Access9 (2021), 135102–135120.
