This paper deals with fuzzy clique covers in fuzzy graphs. The definition of a fuzzy clique is modified so that the fuzzy subgraph induced by each fuzzy clique is complete. Then, fuzzy cliques and maximal fuzzy cliques are characterized. Finally, fuzzy clique covers and minimum fuzzy clique covers in fuzzy graphs are introduced and characterized, and an algorithm to find a minimum fuzzy clique cover of a given fuzzy graph is also presented.
AkramM., Bipolar fuzzy graphs, Information Sciences181 (2011), 5548–5564.
2.
AkramM., Bipolar fuzzy graphs with applications, Knowledge-Based Systems39 (2013), 1–8.
3.
AkramM., ChenW.J. and DavvazB., On N-hypergraphs, Journal of Intelligent and Fuzzy Systems26 (2014), 2937–2944.
4.
AnjaliN. and MathewS., On blocks and stars in fuzzy graphs, Journal of Intelligent & Fuzzy Systems28 (2015), 1659–1665.
5.
BhutaniK.R. and RosenfeldA., Strong arcs in fuzzy graphs, Information Sciences152 (2003), 319–322.
6.
BhutaniK.R. and BattouA., On M-strong fuzzy graphs, Information Sciences155 (2003), 103–109.
7.
BlueM., BushB. and PuckettJ., Unified approach to fuzzy graph problems, Fuzzy Sets and Systems125 (2002), 355–368.
8.
BondyJ.A. and MurtyU.S.R., Graph Theory, Springer, Berlin, 2008.
9.
Di NolaA., SessaS, PedryczW and SanchezE, Fuzzy Relation Equations and Their Applications to Knowledge Engineering, Kluwer Academic Publishers, Boston, 1989.
10.
GómezD., MonteroJ. and YáńezJ., A coloring fuzzy graph approach for image classification, Information Sciences176 (2006), 3645–3657.
11.
GrossG., NagiR. and SambhoosK., A fuzzy graph matching approach in intelligence analysis and maintenance of continuous situational awareness, Information Fusion18 (2014), 43–61.
12.
KóczyL.T., Fuzzy graphs in the evaluation and optimization of networks, Fuzzy Sets and Systems46 (1992), 307–319.
13.
LiuW.J., The realizable problem for symmetric matrix, Fuzzy Mathematics1 (1982), 69–76. (in Chinese).
14.
LiuX.C., The least upper bound of content for realizable matrices on lattice [0,1], Fuzzy Sets and Systems80 (1996), 257–259.
15.
ManjushaO.T. and SunithaM.S., Notes on domination in fuzzy graphs, Journal of Intelligent & Fuzzy Systems27 (2014), 3205–3212.
16.
MathewS. and SunithaM.S., Types of arcs in a fuzzy graph, Information Sciences179 (2009), 1760–1768.
17.
MathewS. and SunithaM.S., Node connectivity and arc connectivity of a fuzzy graph, Information Sciences180 (2010), 519–531.
18.
MathewS. and SunithaM.S., Menger’s theorem for fuzzy graphs, Information Sciences222 (2013), 717–726.
19.
MathewS. and SunithaM.S., Cycle connectivity in fuzzy graphs, Journal of Intelligent & Fuzzy Systems24 (2013), 549–554.
20.
MichaelT.S. and QuintT., Sphericity, cubicity, and edge clique covers of graphs, Discrete Applied Mathematics154 (2006), 1309–1313.
21.
MoY. and WangX.P., An improved algorithm on the content of realizable fuzzy matrices, Soft Comput15 (2011), 1835–1843.
22.
MordesonJ.N. and NairP.S., Cycles and cocycles of fuzzy graphs, Information Sciences90 (1996), 39–49.
23.
MordesonJ.N., NairP.S., Fuzzy Graphs and Fuzzy Hypergraphs, Springer, Berlin, 2000.
24.
MordesonJ.N. and PengC.S., Operations on fuzzy graphs, Information Sciences79 (1994), 159–170.
25.
NairP.S. and ChengS.C., Cliques and fuzzy cliques in fuzzy graphs, Joint 9th IFSA World Congress and 20th NAFIPS International Conference, Vancouver, Canada, 2001, pp. 2277–2280.
26.
PullmanN.J., In Combinatorial Mathematics X, Clique coverings of graphs-a survey, Springer, Berlin, Heidelberg, 1983, 72–85.
27.
RobertsF.S., Applications of edge coverings by cliques, Discrete Applied Mathematics10 (1985), 93–109.
28.
RosenfeldA., Fuzzy graphs, In: ZadehL.A, FuK.S, ShimuraM (Eds.), Fuzzy Sets and Their Alications, Academic Press, New York, 1975, pp. 77–95.
29.
RosyidaI., IndratiC.R. and SugengK.A., A new approach for determining fuzzy chromatic number of fuzzy graph, Journal of Intelligent & Fuzzy Systems28 (2015), 2331–2341.
30.
SamantaS. and PalM., Fuzzy planar graphs, IEEE Transaction on Fuzzy Systems23 (2015), 1936–1942.
31.
SamantaS., PalM. and AkramM., m-step fuzzy competition graphs, Journal of Applied Mathematics and Computing47 (2015), 461–472.
32.
SunF., QuX.B., WangT.F. and WangX.P., Applications of realizable Boolean matrices in graph theory, In: edryczW, ReformatM.Z., (Eds.), Proc 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), Edmonton, Canada, 2013, pp. 843–847.
33.
SunithaM.S. and KumarA.V., Complements of fuzzy graphs, Indian J Pure Appl Math33 (2002), 1451–1464.
34.
WangX.P., How to calculate the content for a given realizable fuzzy matrix, Indian J Pure Appl Math31 (2000), 327–339.
35.
WestD.B., Introduction to Graph Theory (Second Edition), Prentice Hall Inc, 2001.
36.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.