FUZZY PERFECT EQUITABLE DOMINATION EXCELLENT TREES

Yıl 2020, Cilt: 10 Sayı: 2, 512 - 520, 01.03.2020

R. Sumathi R. Sujhata R. Sundareswaran

Öz

A set D of vertices of a fuzzy graph G is a Perfect Dominating set if every vertex not in D is adjacent to exactly one vertex in D. In this paper, we discuss the concept of equitable excellent fuzzy graph, fuzzy equitable excellent dominating set γ ef . We introduce fuzzy perfect equitable excellent dominating set γp G - set and then Construction of perfect equitable excellent fuzzy tree is discussed.

Anahtar Kelimeler

Excellent fuzzy graph, fuzzy equitable dominating set γef, fuzzy equitableperfect dominating set γp G

Kaynakça

• Bhutani, K. R. and Rosenfeld, A., (2003), Strong arcs in fuzzy graph, Information sciences, 152, pp.319-322.
• Dharmalingam, K. M., Rani, M. (2014), Equitable Domination in Fuzzy Graphs, International Journal of Pure and Applied Mathematics, Volume: 94, No: 5, pp. 661-667.
• Fricke, G. H., Haynes, T. W., Hedetniemi, S. S., Laskar, R. C., (2002), Excellent trees, Bulletin of ICA, 34, pp.27-38.
• Haynes, T. W., Hedetniemi, S. T., Slater, P. J., (1998), Domination in Graphs: Advanced Topics, Marcel Dekker, New York.
• Mynhardt, C. M, (1999), Vertices contained in every minimum domination set of a tree, J. Graph Theory, 31, pp. 163–177.
• Mark Caay, Esperanza, B., Arugay, (2017), Perfect Equitable Domination of Some Graphs, Interna- tional Mathematical Forum, 12, (18), pp. 891 - 900.
• Sharada, B., (2012), Perfect Domination Excellent Trees, International J. Math. Combin., 2, pp.76-80.
• Somasundaram, A., Somasundaram, S., (1998), Domination in Fuzzy graphs-I, Pattern Recognition letters, 19, pp.787-791.
• Swaminathan, V. and Dharmalingam, K. M., (2011), Degree Equitable Domination on Graphs, Kragu- jevac Journal of Mathematics, 35, (1), pp.177-183.
• Yamuna, (2003), Excellent - Just Excellent - Very Excellent Graphs, Ph.D. thesis, Alagappa University, Karaikudi.