Article
Version 1
Preserved in Portico This version is not peer-reviewed
Vertex Domination in t-Norm Fuzzy Graphs
Version 1
: Received: 9 April 2018 / Approved: 10 April 2018 / Online: 10 April 2018 (08:41:33 CEST)
Version 2 : Received: 20 August 2020 / Approved: 22 August 2020 / Online: 22 August 2020 (04:01:45 CEST)
Version 2 : Received: 20 August 2020 / Approved: 22 August 2020 / Online: 22 August 2020 (04:01:45 CEST)
How to cite: Nikfar, M. Vertex Domination in t-Norm Fuzzy Graphs. Preprints 2018, 2018040119. https://doi.org/10.20944/preprints201804.0119.v1. Nikfar, M. Vertex Domination in t-Norm Fuzzy Graphs. Preprints 2018, 2018040119. https://doi.org/10.20944/preprints201804.0119.v1.
Abstract
For the first time, We do fuzzification the concept of domination in crisp graph on a generalization of fuzzy graph by using membership values of vertices, α-strong edges and edges. In this paper, we introduce the first variation on the domination theme which we call vertex domination. We determine the vertex domination number γv for several classes of t-norm fuzzy graphs which include complete t-norm fuzzy graph, complete bipartite t-norm fuzzy graph, star t-norm fuzzy graph and empty t-norm fuzzy graph. The relationship between effective edges and α-strong edges is obtained. Finally, we discuss about vertex dominating set of a fuzzy tree with respect to a t-norm ⨂ by using the bridges and α-strong edges equivalence.
Keywords
t-norm Fuzzy graph; t-norm; fuzzy tree; bridge; α-strong edges; vertex domination
Subject
MATHEMATICS & COMPUTER SCIENCE, Other
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
