Connected Perfect Domination in Bipolar fuzzy graphs
Abstract
In this paper we introduced and studied the concepts of connected domination γc(G) and tribal connected domination γtc(G) in bipolar fuzzy graphs. We determine the connected perfect domination number for some standard fuzzy graphs with
suitable examples. We investigated the relationship of γc(G) and γtc(G) with other known
parameters of G. Some bounds and some interesting results for the parameters are obtained. Further, we also obtain Nordhaus - Gaddum type results of γc(G). finally, the
tribal connected perfect domination numberγtcp(G) for several classes of biploar fuzzy
graphs are given with suitable example and obtain bounds for the same.
Downloads
References
M. Akram ,Bipolar fuzzy graphs, Information sciences, 181(2011)5548-5564.
M. Akram ,Bipolar fuzzy graphs with applications, Knowledge Based Systems,
(2013)1-8.
M. Akram and W. A. Dudek ,Regular bipolar fuzzy graphs, Neural Computing and
Applications, 1(2012)197-205.
M. Akram, W. A. Dudek and S. Sarwar ,Properties of bipolar fuzzy hypergraphs,
Italian Journal of Pure and Applied Mathematics, 31(2013)426-458.
M. Akram and A. Farooq ,Bipolar fuzzy trees, NTMSCI, 4(3)(2016)58-72.
M. A. Basheer ,Perfect bipolar fuzzy graphs, Sci.J. Math. Computer Sci, 19(2019)120-
G. S. Domke, J. E. Donbar and L. R. Markus ,The Iinverse domination number of a
graph, ARS Combinatoria, 72(2004)149-160.
F. Haray ,Graph theory, Addison Wesley, Third printing, October, 1972.
A. Kaufman ,Basic idea of fuzzy graph, Introduction a La Theorie des Sous- emsembles Flous, paris, Masson et cie Editeurs, (1973).
M. G. Karunambigai, M. Akram, and K. Palanivel ,Domination in bipolar fuzzy
graphs, International conference on fuzzy systems, (2013)7-10.
V. R. Kulli and S. C. Sigarkanti ,Inverse domination in graphs, reprint extract from:
Nat. acad. Sci. Letters, 14(1991)473-475.
V. Mohanaselvi and S. Sivamani ,Paramount domination in bipolar fuzzy graphs,
International Journal of scientic, Engineering research, 7(50)(2016)50-52.
R. Muthuraj, P. J. Jayalakshmi And S. Revathi ,Perfect domination in bipolar fuzzy
graph, International Journal of Mathematical Archive,9(5)(2018)74-77.
R. Muthuraj and Kanimozhi ,Total strong (weak) domination in bipolar fuzzy graph,
International Journal of computational and applied Mathematics, 12(1)(2017)186-
H. Rashmanloua, S. Samanta, M. Pal and R. A. Borzooeid ,A Study on bipolar fuzzy
graphs, Journal of Intelligent Fuzzy Systems, 28(16)( 2015)571-580.
A. Rosenfeld, L. A. Zadeh, K. S. Fu and M. Shimura, (Eds) ,Fuzzy sets and their
applications, Academic Press, New York, (1975)77-95.
S. Samanta and M. Pal ,Irregular bipolar fuzzy graphs, International Journal of
Applications of Fuzzy Sets, 2(2012)91-102.
A. Somasundaram ,Domination in fuzzy graphs-II, Journal of Fuzzy Math ematics,
(2004)281-289.
A. Somasundaram, S. Somasundaran, Domination in fuzzy graphs-I, Pattern Recognition Letters, 19(1998)787-791.
D. Umamageswari and P. Thangaraj,Domination in operation on bipolar fuzzy
Ggraphs, International Journal of Computational Research and Development,
(2)(2017)56-65.
H. L. Yang, S. G. Li, W. H. Yang and Y. Lu ,Notes on bipolar fuzzy graphs, Information Sciences, 242(2013)113-121.
L. A. Zadeh ,Fuzzy sets, Information and Control, 8(1965)338-353.
W. R. Zhang ,Bipolar fuzzy sets, in Proceedings of Fuzzy IEEE. (1998)835-840.
W. R. Zhang ,Bipolar fuzzy sets and relations, A computational Framework for
cognitive modeling and multi agent decision analysis, Froceedings of IEEE. Conf.
(1994)305-309.
Copyright (c) 2021 IJRDO - Journal of Mathematics (ISSN: 2455-9210)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Author(s) and co-author(s) jointly and severally represent and warrant that the Article is original with the author(s) and does not infringe any copyright or violate any other right of any third parties, and that the Article has not been published elsewhere. Author(s) agree to the terms that the IJRDO Journal will have the full right to remove the published article on any misconduct found in the published article.
