International Journal of Mathematics Trends and Technology
Volume 11 | Number 2 | Year 2014 | Article Id. IJMTT-V11P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V11P517
Let G(V,σ,μ) be a simple undirected fuzzy graph. A subset S of V is called a dominating set in G if every vertex in V-S is adjacent to at least one vertex in S. A subset S of V is said to be a restrained dominating set if every vertex in V-S is adjacent to atleast one vertex in S as well as adjacent to atleast one vertex in V-S. The restrained domination number of a fuzzy graph G(V,σ,μ) is denoted by γ_(fr )(G) which is the smallest cardinality of a restrained dominating set of G. The minimum number of colours required to colour all the vertices such that adjacent vertices do not receive the same colour is the chromatic number χ(G). For any fuzzy graph G a complete fuzzy sub graph of G is called a clique of G. In this paper we find an upper bound for the sum of the Restrained domination and chromatic number in fuzzy graphs and characterize the corresponding extremal fuzzy graphs.
[1] Teresa W. Haynes, Stephen T. Hedemiemi and Peter J. Slater (1998), fundamentals of Domination in fuzzy graphs, Marcel Dekker, Newyork.
[2] Hanary F and Teresa W. Haynes,(2000), Double Domination in fuzzy graphs, ARC Combinatoria 55, pp. 201-213
[3] Haynes, Teresa W.(2001): Paired domination in Fuzzy graphs, Congr. Number 150
[4] Mahadevan G, Selvam A, (2008): On independent domination number and chromatic number of a fuzzy graph, Acta Ciencia Indica, preprint
[5] Paulraj Joseph J. and Arumugam S.(1992): Domination and connectivity in fuzzy graphs, International Journal of Management and systems, 8 No.3: 233-236.
[6] Mahadevan G,(2005): On domination theory and related concepts in fuzzy graphs, Ph.D. thesis, Manonmaniam Sundaranar University,Tirunelveli,India.
[7] Paulraj Joseph J. and Arumugam S.(1997): Domination and colouring in fuzzy graphs. International Journal of Management and Systems, Vol.8 No.1, 37-44.
[8] Paulraj Joseph J, Mahadevan G, Selvam A (2004). On Complementary Perfect domination number of a fuzzy graph, Acta Ciencia India, vol. XXXIM, No.2,847(2006).
[9] Vimala S, Sathya J.S, “Graphs whose sum of Chromatic number and Total domination equals to 2n-5 for any n>4”, Proceedings of the Heber International Conference on Applications of Mathematics and statistics, Tiruchirappalli pp 375-381.
[10] Vimala S, Sathya J.S, “Total Domination Number and Chromatic Number of a Fuzzy Graph”, International Journal of Computer Applications (0975 – 8887) Volume 52– No.3, August 2012.
[11] Vimala S, Sathya J.S, “Connected point set domination of fuzzy graphs”, International Journal of Mathematics and Soft Computing, Volume-2, No-2 (2012),75-78.
[12] Vimala S, Sathya J.S, “Some results on point set domination of fuzzy graphs”, Cybernetics and Information Technologies , Volume 13, No 2 2013 Print ISSN: 1311-9702; Online ISSN: 1314-4081 Bulgarian Academy Of Sciences, Sofia -2013.
[13] Vimala S, Sathya J.S, “The Global Connected Domination in Fuzzy Graphs”, Paripex-Indian Journal of research, Volume 12, Issue: 12, 2013, ISSN - 2250-1991.
[14]Vimala S, Sathya J.S, “Efficient Domination number and Chromatic number of a Fuzzy Graph”, International Journal of Innovative Research in Science, Engineering and Technology, Vol. 3, Issue 3, March 2014, ISSN: 2319-8753.
J.S.Sathya, S.Vimala, "Characterisation of Restrained Domination Number and Chromatic Number of a Fuzzy Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 11, no. 2, pp. 117-123, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V11P517
PDF 
Abstract 
Keywords 
References 
Citation