Abstract
In this Paper, we introduced the concept of fuzzy anti-magic labeling in graphs. We defined Fuzzy Anti-Magic Labeling (FAML) for Cycle, Star, Path and Antiprism graphs.A fuzzy graph G:(σ,μ)s known as fuzzy anti-magic graph if there exists two bijective functions σ : V->[0,1] and μ :V*V ->[0,1] such that μ u,v<σ(u)^σ(v) with the property that the sum of the edge labels incident to each vertex, the sums will all be different. We investigated and verified that fuzzy Cycle graphs, fuzzy Star graphs, fuzzy Path graphs and fuzzy antiprism graphs admits fuzzy anti-magic labeling.Further some properties related to fuzzy bridge and fuzzy cut vertex have been discussed.
Highlights
We begin with a finite, connected and undirected graph G: (σ, μ)without loops and multiple edges
Graph theory has been actively implemented in the fields of Bio-chemistry, Electrical engineering, Computer science, Algebra, Topology and Operations Research
The theory of fuzzy graphs was independently developed by Rosenfeld, Yeh and Bang
Summary
We begin with a finite, connected and undirected graph G: (σ, μ)without loops and multiple edges. Throughout this paper σ(G) and μ(G) denote the vertices and edges respectively. The theory of fuzzy graphs was independently developed by Rosenfeld, Yeh and Bang. Fuzzy graph theory is finding extensive applications in modeling real time systems where the level of information congenital in the system varies with different levels of precision. Nagoorgani et al [2] introduced the concept of fuzzy magic labeling and properties of fuzzy labeling. Akram et al introduced interval valued fuzzy graphs, Strong intuitionistic fuzzy graphs, m-polar fuzzy graphs and novel properties of fuzzy labeling graphs [3]. Already we published two articles in fuzzy Bi-magic labeling and Interval valued fuzzy Bi-magic labeling [4,5]. We introduced the concept of Fuzzy anti-magic labeling on some standard graphs
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