Classification of graphs based on homotopy equivalence. Homotopy equivalent graphs. Basic graphs and complexity of homotopy equivalence classes of graphs
نویسنده
چکیده
The main concept of this classification is that graphs belonging to the same equivalence class have similar topological properties. Graphs are called homotopy equivalent if one of them can be converted to the other one by contractible transformations. A basic representative and complexity of a homotopy equivalence class are defined and investigated. Finding a basic representative within a homotopy equivalence class simplifies many topological problems in digital imaging. A method is designed for the classification of graphs by complexity and basic representatives. This method relies on computer experiments which show that contractible transformations are a graph analogue of homotopy in algebraic topology. Diagrams are given of basic representatives with the complexity N≤6.
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