— In this paper, new concepts are introduced to enhance the process of block identification in fuzzy graphs using sum distance metric and special type of cycles, which is called a strongest strong cycle, locamin cycle. An Algorithm is developed for retrieving information from Big-Data using block identification.
AkramM., Interval-valued fuzzy line graphs, Neural Comput. Appl21 (2012), 145–150.
4.
Banerjee, Saibal, An optimal algorithm to find the degrees of connectedness in an undirected edge-weighted graph, Pattern Recognition Letters12 (1991), 421–424.
5.
BhattacharyaP., SuraweeraF., An algorithm to compute the max-min powers and a property of fuzzy graphs, Pattern Recognit. Lett. 12 (1991), 413–420.
6.
BhutaniK.R., and RosenfeldA, Fuzzy end nodes in fuzzy graphs, Inf. Sci. 152 (2003), 323–326.
7.
BhutaniK.R., On automorphisms of fuzzy graphs, Pattern Recognit. Lett. 9 (1989), 159–162.
8.
BhutaniK.R., and RosenfeldA, Strong arcs in fuzzy graphs, Inf. Sci. 152 (2003), 319–322.
9.
GhoraiG., and Pal, Madhumangal, On degrees of m-polar fuzzy graphs with application, Journal of Uncertain Systems11 (2017), 294–305.
MathewS., AnjaliN., On blocks and stars in fuzzy graphs, Journal of Intelligent & Fuzzy Systems28 (2015), 1659–1665.
12.
MathewS., SunithaM.S., Bonds in graphs and fuzzy graphs, Adv. Fuzzy Sets Syst. 6(2) (2010), 107–119.
13.
MathewS., SunithaM.S., Types of arcs in a fuzzy graph, Inf. Sci. 179(11) (2009), 1760–1768.
14.
MathewS., SunithaM.S., A characterization of blocks in fuzzy graphs, J. Fuzzy Math. 19(1) (2011), 999–1006.
15.
MathewS., SunithaM.S., Strongest strong cycles and θ-fuzzy graphs, IEEE Transactions on Fuzzy Systems21(6) (2013), 1096–1104.
16.
MordesonJ.N., NairP.S., Arc disjoint fuzzy graphs, in Proc. 18th Int. Conf. North Amer. Fuzzy Inf. Process. Soc., 1999, pp. 65–69.
17.
MordesonJ.N., NairP.S., Fuzzy Graphs and Fuzzy Hypergraphs New York, NY, USA: Physica-Verlag, 2000.
18.
SarwarM., AkramM., An algorithm for computing certain metrics in intuitionistic fuzzy graphs, Journal of Intelligent & Fuzzy Systems30 (2016), 2405–2416.
19.
RosenfeldA., Fuzzy graphs, Fuzzy Sets and Their Applications to Cognitive and Decision Processes. ZadehL.A.et al., Eds., New York, NY, USA, Academic, 1975, pp. 77–95
.
20.
SunithaM.S., VijayakumarA., A characterization of fuzzy trees, Inf. Sci. 113 (1999), 293–300.
21.
SunithaM.S., VijayakumarA., Some metric aspects of fuzzy graphs, in Proc. Conf. Graph Connect, 1999, pp. 111–114.
22.
SunithaM.S., VijayakumarA., Complement of a fuzzy graph, Indian J. Pure Appl. Math33(9) (2002), 1451–1464.
23.
SunithaM.S., VijayakumarA., Blocks in fuzzy graphs, J. Fuzzy Math13(1) (2005), 13–23.
24.
PandeyS., TokekarV., Prominence of MapReduce in BIG DATA Processing. In Fourth International Conference on Communication Systems and Network Technologies, IEEE, 2014, pp. 555–560.
25.
TomM., SunithaS., Sum distance in fuzzy graphs, Annals of Pure and Applied Mathematics7(2) (2014), 73–89.
26.
TongZ., ZhengD., An algorithm for finding the connectedness matrix of a fuzzy graph, Congr. Numer. 120 (1996), 189–192.
27.
YehR.T., BangS.Y., Fuzzy relations, fuzzy graphs and their applications to clustering analysis, Fuzzy Sets and Their Applications. ZadehL.A., et al., Eds., New York, NY, USAAcademic, 1975, pp. 125–149
.
