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Weak Graph Map Homotopy and Its Applications

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The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and applications.They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001.The difference between them is that the weak graph map homotopy transformation is defined in terms of maps,while the graph homotopy transfor-mation is defined by means of combinatorial operations.They discuss its advantages over the graph homotopy transformation.As its applications,they investigate the mapping class group of a graph and the 1-order MP-homotopy group of a pointed simple graph.Moreover,they show that the 1-order MP-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.

Weak graph map homotopyTrivial vertexStrong deformation retractMapping class groupMP-Homotopy group

Conglei ZHANG、Yanying WANG、Zhiguo ZHANG、Yan ZHAO

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School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China

Department of Basic Science,Shanxi Agricultural University,Jinzhang 030801,Shanxi,China

Center for Topology and Geometry based Technology,School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China

School of Mathematics and Computer Science,Shanxi Normal University,Taiyuan 030031,China

School of Mathematics and Science,Hebei GEO University,Shijiazhuang 050031,China

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国家自然科学基金

11771116

2024

10.1007/s11401-024-0014-8

数学年刊B辑(英文版)
国家教育部委托复旦大学主办

数学年刊B辑(英文版)

CSTPCD
影响因子：0.129
ISSN：0252-9599
年,卷(期)：2024.45(2)
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