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FUZZY PERFECT EQUITABLE DOMINATION EXCELLENT TREES

Year 2020, Volume: 10 Issue: 2, 512 - 520, 01.03.2020

Abstract

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.

References

  • 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.
Year 2020, Volume: 10 Issue: 2, 512 - 520, 01.03.2020

Abstract

References

  • 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.
There are 10 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

R. Sumathi This is me

R. Sujhata This is me

R. Sundareswaran This is me

Publication Date March 1, 2020
Published in Issue Year 2020 Volume: 10 Issue: 2

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