This paper considers networks as wireless sensor (hyper)networks and social (hyper)networks by single–valued neutrosophic (directed)(hyper)graphs.The notion of single–valued neutrosophic hypergraphs are extended to single–valuedneutrosophic directed hypergraphs and conversely. We derived single–valued neutrosophic digraphs from single–valued neutrosophic directed hypergraphs via a positive equivalence relation. It tries to use single–valued neutrosophic directed hypergraphs and positive equivalence relation to create the sensor clusters and to access to cluster heads in wireless sensor (hyper)networks. Finally, the concept of α-derivable single–valued neutrosophic digraph is considered as the energy-efficient protocol of wireless sensor networks and is applied this concept as a tool in wireless sensor (hyper)networks.
AkramM., ShahzadiS. and Borumand SaeidA., Neutrosophic hypergraphs, TWMS J App Eng Math8(1) (2018), 122–135.
2.
AkramM. and LuqmanA., Certain concepts of bipolar fuzzy directed hypergraphs, Mathematics5(1) (2017).
3.
AkramM. and LuqmanA., Certain network models using single-valued neutrosophic directed hypergraphs, Journal of Intelligent and Fuzzy Systems33(1) (2017), 575–588.
4.
AkramM. and LuqmanA., Directed hypergraphs under mpolar fuzzy environment, Journal of Intelligent and Fuzzy Systems34(6) (2018), 4127–4137.
5.
AkramaM., SarwaraM. and BorzooeiR.A., A novel decision-making approach based on hypergraphs in intuitionistic fuzzy environment, Journal of Intelligent & Fuzzy Systems35(2) (2018), 1905–1922.
6.
AkramM. and DudekW.A., Intuitionistic fuzzy hypergraphs with applications, Information Sciences218 (2013), 182–193.
7.
AkramM. and SarwarM., Novel applications of m-polar fuzzy hypergraphs, Journal of Intelligent and Fuzzy Systems32(3) (2016), 2747–2762.
8.
AkramM., ShahzadiS. and Borumand SaeidA., single– valued neutrosophic hypergraph, TWMS J App Eng Math8(1) (2018), 122–135.
9.
BergeC., Graphs and Hypergraphs, North Holland, 1979.
10.
DevadossA.V., RajkumarA. and PraveenaN.J.P., A study on miracles through holy bible using neutrosophic cognitive maps (NCMS), International Journal of Computer Applications69(3) (2013).
11.
GalloG., LongoG. and PallottinoS., Directed hypergraphs and applications, Discrete Appl. Math42 (1993), 177–201.
12.
HamidiM. and Borumand SaeidA., Creating and computing graphs from hypergraphs, Kragujevac Journal of Mathematics43(1) (2019), 139–164.
13.
HamidiM. and Borumand saeidA., On derivable trees, Transactions on Combinatorics (2019) (accepted).
14.
HamidiM. and Borumand SaeidA., Accessible single-valued neutrosophic graphs, J Appl Math Comput57 (2018), 121–146.
15.
HamidiM. and Borumand SaeidA., Achievable single-valued neutrosophic graphs in wireless sensor networks, New Mathematics and Natural Computation14(2) (2018), 157–185.
16.
MajumdarP. and SamantaS.K., On similarity and entropy of neutrosophic sets, Journal of Intelligent & Fuzzy Systems26(3) (2014), 1245–1252.
17.
RashmanlouH., SahooS., BorzooeiR.A., PalM. and LakdashtiA., Computation of shortest path in a vague network by euclidean distance, Journal of Mult-Valued Logic and Soft Computing30 (2017), 115–123.
18.
SahooS. and PalM., Certain types of edge irregular intuitionistic fuzzy graphs, Journal of Intelligent and Fuzzy Systems34(1) (2018), 295–305.
19.
SahooS. and PalM., Different types of products on intuitionistic fuzzy graphs, Pacific Science Review A: Natural Science and Engineering17(3) (2015), 87–96.
20.
SahooS. and PalM., Intuitionistic fuzzy competition graph, Journal of Applied Mathematics and Computing52 (2015), 37–57.
21.
SahooS. and PalM., Intuitionistic fuzzy tolerance graph with application, Journal of Applied Mathematics and Computing55 (2016), 495–511.
22.
SahooS. and PalM., Modular and homomorphic product of intuitionistic fuzzy graphs and their degree, International Journal of Computing Science and Mathematics8(5) (2017), 395–404.
23.
SahooS. and PalM., Product of intuitionistic fuzzy graphs and degree, Journal of Intelligent and Fuzzy Systems32(1) (2016), 1059–1067.
24.
SahooS., PalM., RashmanlouH. and BorzooeiR.A., Covering and paired domination in intuitionistic fuzzy graphs, Journal of Intelligent and Fuzzy Systems33(6) (2017), 4007–4015.
25.
SahooS., GhoraiG. and PalM., Embedding and genus of intuitionistic fuzzy graphs on spheres, Journal of Mult.-Valued Logic and Soft Computing31 (2018), 139–154.
26.
SmarandacheF., Neutrosophy neutrosophic probability, Set and Logic, Amer Res Press, Rehoboth, USA, 1998.
27.
SmarandacheF., A unifying field in logics, Neutrosophy: Neutrosophic probability, set and logic, American Research Press, Rehoboth, 1999.
28.
SmarandacheF., Refined literal indeterminacy and the multiplication law of sub-indeterminacies, Neutrosophic Sets and Systems9 (2015), 58.
29.
SmarandacheF., Symbolic Neutrosophic Theory, Europanova asbl, Brussels, p. 195.
30.
Vasantha KandasamyW.B. and IlanthenralK., Florentin Smarandache Neutrosophic Graphs, A New Dimension to Graph Theory, Kindle Edition, 2015.
31.
WangH., SmarandacheF., ZhangY. and SunderramanR., Single valued neutrosophic sets, Multisspace and Multistructure4 (2010), 410–413.
32.
WangH., SmarandacheF., ZhangY.Q. and SunderramanR., Single-valued neutrosophic sets, Multisspace and Multistruct4 (2010), 410–413.
33.
ZadehL.A., Fuzzy sets, Information and Control8(3) (1965), 338–353.
