Fuzzy Systems

G. Geetha Ramani ¹, N. Vinoth Kumar ¹

Affiliations
1 Department of Mathematics, Anna University of Technology, Trichy, IN

Abstract

Let G:(,μ) be a fuzzy graph with SV is a dominating set of G and the dominating number (G).In this paper we define the strong edge dominating set D’ VV in G, we introduce a edge dominating number ’(G) is a minimum cardinality of edge dominating set of G. we prove some results in strong edge domination.

Keywords

Fuzzy Graphs, Fuzzy Strong (ARC) Edge Domination, Strong (Weak) Edge Domination, Fuzzy Strong (ARC) Edge Domination Number, Strong (Weak) Fuzzy Edge Domination Number.

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N. Vinoth Kumar ¹, G. Geetha Ramani ²

Affiliations
1 M.A.M.School of Engineering, Trichy, Tamilnadu, 620105, IN
2 Anna University of Technology, Trichy, Tamilnadu, 620024, IN

Abstract

Let G:(,μ) be a fuzzy graph with D V is a dominating set of G and the dominating number (G). In this paper we define the inverse fuzzy dominating set D’ VV in G, we introduce a inverse fuzzy dominating number f-1(G) is a minimum cardinality of inverse fuzzy dominating set of G. we prove some results in inverse fuzzy domination.

Keywords

Fuzzy Graphs, Inverse Fuzzy Strong Domination, Inverse Fuzzy Domination Number, Split and Non-Split Domination in Fuzzy Graph.

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N. Vinoth Kumar ¹, G. Geetha Ramani ²

Affiliations
1 M.A.M. School of Engineering, Trichy, Tamilnadu–621 104, IN
2 Anna University of Technology, Trichy, Tamilnadu–620 024, IN

Abstract

Let G: (σ, μ) be a fuzzy graph. A set D of V is said to be fuzzy dominating set of G if every v ε V-D there exit u ε D such that u dominates v. Let u and v be any two vertices of a fuzzy graph G. Then u strongly dominates v (v weakly dominates u) if (i) μ (u, v) = σ (u) σ(v) and (ii) d N (u) ≥ d N (v).Let G be a fuzzy graph. Then D V is said to be a strong (weak) fuzzy dominating set of G if every vertex v є V − D is strongly (weakly) dominated by some vertex u in D. In this paper we investigate the changes in the fuzzy cardinality of above dominating sets, when we remove the vertex in the graph G.

Keywords

Domination Critical, Strong (Weak) Domination Critical.

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