Preprint Article Version 1 This version is not peer-reviewed

Nikfar Domination in Fuzzy Graphs

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)

How to cite: Nikfar, M. Nikfar Domination in Fuzzy Graphs. Preprints 2019, 2019010024 (doi: 10.20944/preprints201901.0024.v1). Nikfar, M. Nikfar Domination in Fuzzy Graphs. Preprints 2019, 2019010024 (doi: 10.20944/preprints201901.0024.v1).

Abstract

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.

Subject Areas

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

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.