Strong homotopy induced by adjacency structure (Q2092351)
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scientific article; zbMATH DE number 7611185
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Strong homotopy induced by adjacency structure |
scientific article; zbMATH DE number 7611185 |
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Strong homotopy induced by adjacency structure (English)
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2 November 2022
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The paper under review deals with some thinning of a graph using a strong \(SA\)-deformation retract of a simple graph compared to a strong \(SA\)-homotopic thinning. Besides, the paper proves that two simple graphs are \(SA\)-homotopy equivalent iff they have graph isomorpic cores. In addition, the mapping class group of a graph is introduced and studied. However, since the notion of an \(SA\)-homotopy equivalence on an adjacency-based graph induced by an Alexandroff space is so rigid, we have some limitations of its use in applied sciences or digital geometry.
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strong homotopy on graph
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strong deformation retract
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homotopy transformation
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core of graph
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trivial vertex
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mapping class group
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