Preprint Article Version 1 This version is not peer-reviewed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)

How to cite: Nikfar, M. Vertex Domination in t-Norm Fuzzy Graphs. Preprints 2018, 2018040119 (doi: 10.20944/preprints201804.0119.v1). Nikfar, M. Vertex Domination in t-Norm Fuzzy Graphs. Preprints 2018, 2018040119 (doi: 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.

Subject Areas

t-norm Fuzzy graph; t-norm; fuzzy tree; bridge; α-strong edges; vertex domination

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