A note on edge domination in fuzzy graphs

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DOI:

https://doi.org/10.26637/MJM0804/0114

Abstract

An edge dominating set \(D^{\prime}\) of a fuzzy graph \(G=(\sigma, \mu)\) is an effective edge dominating set if every edge in \(D^{\prime}\) is effective. In the present work, the concept of effective edge domination in fuzzy graphs is introduced. We determine the effective edge domination number \(\gamma^{\prime}(G)\) of some kind of fuzzy graphs. We present some general bounds related to the effective edge domination number. In addition, this new domination is being discussed in the join of fuzzy graphs.

Keywords:

Fuzzy graph, Effective edge, Edge dominating set, Effective edge domination number, Fuzzy cycle, Complete fuzzy graph, Fuzzy path

Mathematics Subject Classification:

Mathematics
  • A. Selvam BCM Government Women’s Polytechnic College, Ettayapuram-628902, Tamil Nadu, India.
  • C.Y. Ponnappan Department of Mathematics, Government Arts College, Melur-625106, Tamil Nadu, India.
  • Pages: 2000-2004
  • Date Published: 01-10-2020
  • Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

L.A. Zadeh, Fuzzy sets, Fuzzy Sets and Control, 8 (1965), 338-353.

C. Berge, Graphs and Hyper Graphs, North-Holland, Amsterdam, 1973.

O.T. Manjusha, M.S. Sunitha, Notes on domination in fuzzy graphs, Journal of Intelligent and Fuzzy Systems, $27(2014), 3205-3212$.

A. Somasundaram and S. Somasundaram, Domination in fuzzy graphs - I, Pattern Recognition Letters, 19(1998), $787-791$.

Oystein Ore, Theory of Graphs, American Mathematical Society Colloquium Publications, Vol. XXXVIII, American Mathematical Society, Providence, R.I., 1962.

A. Rosenfeld, Fuzzy Graphs, Academic Press, New York, 1975.

E. Harary, Graph Theory, Addison Wesley, 1989.

S. Mathew and M.S. Sunitha, Types of arcs in a fuzzy graph, Information Sciences, 179 (2009), 1760-1768.

Bhutani, K.R. and Rosenfeld. A, Strong arcs in fuzzy graph, Information Sciences, 152(2003), 319-322.

S. Mitchell and S. T. Hedetniemi, Edge domination in trees, Gongr. Numer., 19 (1977), 489-509.

S. Arumugam and S. Velammal, Edge domination in graphs, Taiwanese Journal of Mathematics, 2(2)(1998), 173-179.

  • NA

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Published

01-10-2020

How to Cite

A. Selvam, and C.Y. Ponnappan. “A Note on Edge Domination in Fuzzy Graphs”. Malaya Journal of Matematik, vol. 8, no. 04, Oct. 2020, pp. 2000-4, doi:10.26637/MJM0804/0114.