Generalized Fuzzy Magic Labeling

Abstract

Let G=(V,E)andH =(V′,E′)besimple, finite, planar, connected, and undirected graphs with the property that each edge of G belongs to at least one subgraph of G∗ isomorphic to H. Then G=(σ,µ) is called a fuzzy labeling graph on G∗, if σ :V → [0,1] and µ : E → [0,1] are one-to-one maps, and for all xy ∈ E: µ(xy) < σ(x)∧σ(y) Afuzzy labeling graph G = (σ,µ) on G∗ is called an H-fuzzy magic labeling graph if there exists m ∈ (0,v′+e′) such that for any subgraph H′ of G isomorphic to H: ∑ x∈V′ σ(x)+ ∑ y∈E′ σ(y) =m In this report, we will generalize fuzzy H-magic labeling of H-super magic labeling by normalizing H-super magic labelings.