In this paper, some new connectivity concepts in fuzzy labeling graphs are defined. The concepts of strong arc, partial cut node, bridge and block are introduced. A new type of fuzzy labeling graphs called θ-fuzzy labeling graphs is defined. Likewise, this paper generalizes the tree concept in fuzzy labeling graph, which plays a crucial role in many areas of science and technology.
BorzooeiR.A. and RashmanlouH., Ring sum in product intuitionistic fuzzy graphs, Journal of Advanced Research in Pure Mathematics7(1) (2015), 16–31.
2.
BorzooeiR.A. and RashmanlouH., Domination in vague graphs and its applications, Journal of Intelligent and Fuzzy Systems, to appear.
3.
Nagoor GaniA., AkramM. and Rajalami(a)SubahashiniD., Novel properties of fuzzy labeling graphs, Journal of Mathematics (2014), 1–6. Article ID 375135.
4.
PalM. and RashmanlouH., Irregular interval-valued fuzzy graphs, Annals of Pure and Applied Mathematics3(1) (2013), 56–66.
5.
RashmanlouH. and PalM., Antipodal interval-valued fuzzy graphs, International Journal of Applications of Fuzzy Sets and Artificial Intelligence3 (2013), 107–130.
6.
RashmanlouH. and PalM., Balanced interval-valued fuzzy graph, Journal of Physical Sciences17 (2013), 43–57.
7.
RashmanlouH., SamantaS., PalM. and BorzooeiR.A., A study on bipolar fuzzy graphs, Journal of Intelligent and Fuzzy Systems28 (2015), 571–580.
8.
RashmanlouH., SamantaS., PalM. and BorzooeiR.A., Bipolar fuzzy graphs with categorical properties, International Journal of Computati Intelligence Systems8(5) (2015), 808–818.
9.
RashmanlouH. and JunY.B., Complete interval-valued fuzzy graphs, Annals of Fuzzy Mathematics and Informatics6(3) (2013), 677–687.
10.
RosenfeldA., Fuzzy graphs, Fuzzy Sets and their Applications, (ZadehL.A., FuK.S. and ShimuraM., Eds.), Academic Press, New York, 1975, pp. 77–95.
11.
SamantaS. and PalM., Fuzzy planar graphs, IEEE Transaction on Fuzzy Systems, 23(6) (2015), 1936–1942.
12.
SamantaS., PalM. and AkramM., m-step fuzzy competition graphs, Journal of Applied Mathematics and Computing, 47 (2015), 461–472.
13.
SamantaS. and PalM., Fuzzy tolerance graphs, Int J Latest Trend Math1(2) (2011), 57–67.
14.
SamantaS. and PalM., Fuzzy threshold graphs, CiiT International Journal of Fuzzy Systems3(12) (2011), 360–364.
15.
SamantaS., PalM. and PalA., New concepts of fuzzy planar graph, International Journal of Advanced Research in Articial Intelligence3(1) (2014), 52–59.
16.
SamantaS. and PalM., Fuzzy k-competition graphs and p-competition fuzzy graphs, Fuzzy Engineering and Information5(2) (2013), 191–204.
17.
SamantaS. and PalM., Irregular bipolar fuzzy graphs, Int J Appl Fuzzy Sets2 (2012), 91–102.
18.
SamantaS., PramanikT. and PalM., Fuzzy colouring of fuzzy graphs, Afrika Matematika. DOI: 10.1007/s13370-015-0317-8.
19.
SunithaM.S. and VijayakumarA., Complement of a fuzzy graph, Indian Journal of Pure and Applied Mathematics33(9) (2002), 1451–1464.
20.
YehR.T. and BangS.Y., Fuzzy relations, fuzzy graphs and their application to clustering analysis, Academic Press, New York, 1975, pp. 125–149
.
21.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.
