Strong homotopy induced by adjacency structure
type: Item
instance of: scholarly article
title: Strong homotopy induced by adjacency structure
author: Yanyan Li
published in: Discrete Mathematics
publication date: 2022-11-02T00:00:00Z
review text: 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.
reviewed by: Sang-Eon Han
Mathematics Subject Classification ID: 55P10
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 68U05
Mathematics Subject Classification ID: 54H30
zbMATH DE Number: 7611185
zbMATH Keywords: strong homotopy on graph
zbMATH Keywords: strong deformation retract
zbMATH Keywords: homotopy transformation
zbMATH Keywords: core of graph
zbMATH Keywords: trivial vertex
zbMATH Keywords: mapping class group
MaRDI profile type: Publication
full work available at URL: j.disc.2022.113130
OpenAlex ID: W4293113749
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DOI: 10.1016/J.DISC.2022.113130
description: scientific article; zbMATH DE number 7611185