Open Journal Systems

Degree Equitable Connected Domination in Fuzzy Graphs

K.M. Dharmalingam M. Rani

crossmark logo side by side horizontal


Let  be a fuzzy graph. Let  and  be two vertices of . A fuzzy connected dominating set  is to be a fuzzy equitable connected dominating set if for every  there exists a vertex  such that  and  where  denotes degree of vertex  and  denotes the degree of vertex  and . The minimum cardinality of fuzzy equitable connected domination set is denoted by . In this paper we introduce the concept of fuzzy equitable connected dominating set. Also we obtain some interesting results for this new parameter in equitable connected domination in fuzzy graphs.

Full Text:



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

K.M. Dharmalingam and M.Rani, Equitable Domination in Fuzzy Graphs, International Journal of Pure and Applied Mathematics, Volume 94 (No. 5) 2014, 661-667

Kuppusamy Markandan Dharmalingam, Equitable Associate Graph of a Graph, Bulletin of International Mathematical Virtual Institue 2(1)(2012) 109-116

J.N Mordeson and P.S Nair, Fuzzy graphs and Fuzzy Hyper graphs, Physica Verlag, Heidelberg, 1998, Second edition 2001

A. Nagoor Gani and V.T. Chandra Sekaran, Domination in Fuzzy Graph, Advances in Fuzzy Sets and Systems, 1(1)(2006), 17-26

A. Nagoor Gani, P. Vadivel, Contribution to the theory of Domination, Independence and Irredundance in Fuzzy graph, Bulletin of Pure and Applied Sciences, Vol-28E (No-2) 2009, 179-187

A Rosenfield, Fuzzy graphs, in, L.A.Zadeh, K.S. Fu, M.Shimura (Eds), Fuzzy sets and their Applications to congnitive and Decision Processes, Academic Press, New York, 1975, 77-95

E. Sampath Kumar, L.Puspalatha, Strong, weak domination and domination balance in a graph, Discrete Math. 161(1966) 235 - 242

A. Somasundaram and S.Somasundaram, Domination in Fuzzy Graphs-I, Elsevier Science, 19(1998), 787-791

Vekatasubramanian Swaminathan and Kuppusamy Markandan Dharmalingam, Degree Equitable Domination on Graphs, Kragujevac Journal of Mathematics, Volume 35, Number 1, PP 177-183, (2011)



  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.