Nikfar Domination in Fuzzy Graphs

Mohammadesmail Nikfar

doi:10.20944/preprints201901.0024.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 31 December 2018 / Approved: 3 January 2019 / Online: 3 January 2019 (13:43:25 CET)
Version 2 : Received: 28 April 2019 / Approved: 7 May 2019 / Online: 7 May 2019 (10:14:31 CEST)
Version 3 : Received: 13 May 2019 / Approved: 14 May 2019 / Online: 14 May 2019 (09:50:12 CEST)

We introduce a new variation on the domination theme which we call nikfar domination as reducing waste of time in transportation planning. We determine the nikfar domination number v for several classes of fuzzy graphs. The bounds is obtained for it. We prove both of the Vizing's conjecture and the Grarier-Khelladi's conjecture are monotone decreasing fuzzy graph property for nikfar domination. We obtain Nordhaus-Gaddum (NG) type results for these parameters. Finally, we discuss about nikfar dominating set of a fuzzy tree by using the bridges and -strong edges equivalence.

fuzzy graph, fuzzy bridge, -strong edge, nikfar domination, dynamic networks

Computer Science and Mathematics, Computer Vision and Graphics

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Nikfar Domination in Fuzzy Graphs

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