7.3 Isomorphisms of Interval-Valued Fuzzy Graphs In this section, we consider various types of (weak) isomorphisms of interval-valued fuzzy graphs. Definition 7.3.1 Let G₁ = (A₁, B₁) and G₂ = (A2, B₂) be two interval-valued fuzzy graphs. A homomorphism f: G₁ G₂ is a mapping f: V₁ → V₂ such that for all x₁ € V₁, X1y1 € E1, (i) μÃ, (x₁) ≤μÃ₂ (f (x₁)), μ, (x₁) ≤ μ₂ (f(x₁)), + (ii) μg, (x1Y1) ≤ PB₂ (f(x₁) ƒ (y₁)), µg, (x₁y₁) ≤ ₂ (f(x₁) f (y)). A bijective homomorphism with the property (iii) μA, (x₁) = μÃ₂ (f(x₁)), μ₁ (x₁) = μ₂ (f(x₁)) is called a weak isomorphism and a weak co-isomorphism if = (iv) B₁ (x1y₁) = PB₂ (f(x₁) f (y1₁)), P, (X1Y₁) X1, y1 € V₁. A bijective mapping f: G₁ G₂ satisfying (iii) and (iv) is called an isomor- phism. (f(x₁) f(y)) for all

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