A STUDY ON BONDAGE AND NON BONDAGE NUMBER OF FUZZY GRAPHS AND GRACEFUL GRAPHS

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R. Jahir Hussain

Abstract

Abstract:In this paper, we deï¬ne the bondage bD(G), Co-bondage bDc(G), and Non- bondge bDn(G) number for any fuzzy directed graph and exact values for some standard directed graphs.We also deï¬ne KP bondage of ladder graph and grid graph and we also discussed with fuzzy graceful graph.
Keywords:Minimum dominating set γD(G), maximum non-bondage number bDn(G),minimum bondage number bD(G).

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How to Cite
Hussain, R. J. (2017). A STUDY ON BONDAGE AND NON BONDAGE NUMBER OF FUZZY GRAPHS AND GRACEFUL GRAPHS. Journal of Global Research in Mathematical Archives(JGRMA), 4(10), 50–57. Retrieved from https://jgrma.com/index.php/jgrma/article/view/349
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Review Articles

References

T.L. Baldwin, L. Mili, M.B. Boisen Jr, R. Adapa, Power system observability with minimal phasor measurement placement, IEEE Trans. Power Systems 8 (1993) 707715

E.J.Cockayne, B.L.Hartnell, S.T. Hedetniemi and R. Laskar , Efficient domination in graphs, Technical Report 558 Clemson University, department of mathematical Sciences (1988)

E.J. Cockayne and S.T Hedetniemi; Towards a theory of domination in graphs,Networks,247-261 (1977)

J.F .Fink, M.S.Jacobson, L.F .Kinch and J.Roberts; The bondage number of graph, Discrete Math., 86, 47-57 (1990).

Gerard Jennhwa Chang , Paul Dorbec ,, Mickael Montassier, Andr Raspaud:Generalized power domination of graphs,Discrete Applied Mathematics 160 (2012) 16911698

F. Harary: Graph theory , Addison Wesley , Reading, Massachusetts (1963) [7] R.JahirHussain and R.M. Karthik keyan: Characterization of fuzzy non- bondage number

of fuzzy graphs. Mathematical Sciences int., Research Journal vol4 issue 2 ISSN 2278-8697 [8] V.R. Kulli and B. Janakiram; The non-bondage number of a graph , New York Acadency of Science, (1996)

A.Rosenfeld. Fuzzy graphs, InFuzzysets and their applications to Cognitive and Decision.Eds. Academic press, New York (1975)77-95.

K .R. Sandeep Narayan and M.S. Sunitha ; Connectivity in a Fuzzy Graph and its complement ICSRS Publication ,2012

Sunil Mathew, Sunitha M.S; Fuzzy Graphs: Basic Concepts and Applications, Lap Lambert Academic Publication.

G. Suresh Singh, Sunitha Grace Zacharia : Some Results On Completely Extendable And Weighted Extendable Graphs International Journal Of Mathematical Archive-2016, 92-97 Theory of Domination in Graphs, MRI Lecture Notes Math. I (1979)