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Introduction Chapter One Distances and Hosoya Polynomials of Graphs 1.1. Distance in Graphs 1.2. Generalized Distances in Graphs 1.3. Hosoya Polynomials of Distance in Graphs 1.4. Hosoya Polynomials of Steiner Distance Chapter Two Hosoya Polynomials of Some Particular Graphs 2.1. Complete m-partite Graphs 2.2. Straight Hexagonal Chains 2.3. Hypercube Graphs (m-Cube Qm) 2.4. The Square of a Path (P2T) Chapter Three Hosoya Polynomials of Some Composite Graphs 3.1. The Join of Two Graphs 3.2. Sequential Join of Empty Graphs 3.3. Sequential Join of Complete Graphs 3.4. The Corona of Two Graphs Chapter Four Hosoya Polynomials of Steiner n-Distance of Trees 4.1. A Generalization of Wiener's Theorem for Trees 4.2. Special Complete 2-Ary Trees 4.3, Thorn Stars 4.4. Generalized Thorn Rods 4.5. Thorn Caterpillars 4.6. Banana Trees Chapter Five Hosoya Polynomials of Some Thorn Special Graphs 5.1. Thorn Rings 5.2. Thorn Complete Graphs 5.3. Thorn Complete Bipartite Graphs 5.4. Thorn Wheels Chapter Six Hosoya Polynomials of the Composite Graphs G1¡õ(ÌØÊâ·ûºÅ)G2 6.1. The Composite Graph Ka¡õ(ÌØÊâ·ûºÅ)K¦Â 6.2. The Composite Graph Ka¡õ(ÌØÊâ·ûºÅ)K¦Â,¦Ã 6.3. The Composite Graph Wa¡õ(ÌØÊâ·ûºÅ)K¦Â 6.4. The Composite Graph Ca¡õ(ÌØÊâ·ûºÅ)K¦Â References ±à¼­ÊÖ¼Ç