About Vertex Mappings

6533b85cfe1ef96bd12bd410

RESEARCH PRODUCT

About Vertex Mappings

subject

graph isomorphism Vertex (graph theory)05c60 Applied Mathematics 68t99 Combinatorics Computational Mathematics graph homomorphism 03b35 QA1-939 Graph homomorphism Graph isomorphism Mathematics MathematicsofComputing_DISCRETEMATHEMATICS Mathematics

description

Summary In [6] partial graph mappings were formalized in the Mizar system [3]. Such mappings map some vertices and edges of a graph to another while preserving adjacency. While this general approach is appropriate for the general form of (multidi)graphs as introduced in [7], a more specialized version for graphs without parallel edges seems convenient. As such, partial vertex mappings preserving adjacency between the mapped verticed are formalized here.

year	journal	country	edition	language
2019-10-01	Formalized Mathematics

https://doi.org/10.2478/forma-2019-0025

PEPhysical Sciences and Engineering
- PE2Fundamental Constituents of Matter
  - PE2_1Theory of fundamental interactions
  - PE2_2 Phenomenology of fundamental interactions
  - PE2_3Experimental particle physics with accelerators
  - PE2_4Experimental particle physics without accelerators
  - PE2_6Nuclear, hadron and heavy ion physics
  - PE2_8Gas and plasma physics
  - PE2_5Classical and quantum physics of gravitational interactions
  - PE2_7Nuclear and particle astrophysics
  - PE2_9 Electromagnetism
  - PE2_10Atomic, molecular physics
  - PE2_11Ultra-cold atoms and molecules
  - PE2_18Equilibrium and non-equilibrium statistical mechanics: steady states and dynamics
  - PE2_14Lasers, ultra-short lasers and laser physics
  - PE2_17Metrology and measurement
  - PE2_16Non-linear physics
  - PE2_12Optics, non-linear optics and nano-optics
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- PE1Mathematics
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  - PE1_8Analysis
  - PE1_7Topology
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  - PE1_11Theoretical aspects of partial differential equations
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  - PE1_14Mathematical statistics
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  - PE1_4 Algebraic and complex geometry
  - PE1_19Scientific computing and data processing
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  - PE1_21Application of mathematics in sciences
  - PE1_22Application of mathematics in industry and society
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  - PE1_3Number theory
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  - PE7_1Control engineering
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  - PE10_21Earth system modelling and interactions
  - PE10_14Earth observations from space/remote sensing
  - PE10_11Geochemistry, cosmochemistry, crystal chemistry, isotope geochemistry, thermodynamics
  - PE10_13Physical geography, geomorphology
  - PE10_12Sedimentology, soil science, palaeontology, earth evolution
- PE11Materials Engineering
  - PE11_2Engineering of metals and alloys
  - PE11_1Engineering of biomaterials, biomimetic, bioinspired and bio-enabled materials
  - PE11_3Engineering of ceramics and glasses
  - PE11_4Engineering of polymers and plastics
  - PE11_5Engineering of composites and hybrid materials
  - PE11_6Engineering of carbon materials
  - PE11_7Engineering of metal oxides
  - PE11_8Engineering of alternative established or emergent materials
  - PE11_9Nanomaterials engineering, e.g. nanoparticles, nanoporous materials, 1D & 2D nanomaterials
  - PE11_10Soft materials engineering, e.g. gels, foams, colloids
  - PE11_11Porous materials engineering, e.g. covalent-organic, metal-organic, porous aromatic frameworks
  - PE11_12Semi-conducting and magnetic materials engineering
  - PE11_13Metamaterials engineering
  - PE11_14Computational methods for materials engineering
LSLife Sciences
- LS1Molecules of Life: Biological Mechanisms, Structures and Functions
  - LS1_2Biochemistry
  - LS1_1Macromolecular complexes including interactions involving nucleic acids, proteins, lipids and carbohydrates
  - LS1_3DNA and RNA biology
  - LS1_4Protein biology
  - LS1_5Lipid biology
  - LS1_6Glycobiology
  - LS1_11Chemical biology
  - LS1_12Protein design
  - LS1_13Early translational research and drug design
  - LS1_14Innovative methods and modelling in molecular, structural and synthetic biology
  - LS1_10Synthetic biology
  - LS1_8Structural biology
  - LS1_9Molecular mechanisms of signalling processes
  - LS1_7Molecular biophysics, biomechanics, bioenergetics
- LS2Integrative Biology: from Genes and Genomes to Systems
  - LS2_1Genetics
  - LS2_3Epigenetics
  - LS2_2Gene editing
  - LS2_4Gene regulation
  - LS2_5Genomics
  - LS2_6Metagenomics
  - LS2_7Transcriptomics
  - LS2_8Proteomics
  - LS2_9Metabolomics
  - LS2_10Glycomics/Lipidomics
  - LS2_11Bioinformatics and computational biology
  - LS2_12Biostatistics
  - LS2_14Genetic diseases
  - LS2_16Innovative methods and modelling in integrative biology
  - LS2_13Systems biology
  - LS2_15Integrative biology for personalised medicine
- LS4Physiology in Health, Disease and Ageing
  - LS4_1Organ and tissue physiology and pathophysiology
  - LS4_4Endocrinology
  - LS4_3Physiology of ageing
  - LS4_2Comparative physiology
  - LS4_5Non-hormonal mechanisms of inter-organ and tissue communication
  - LS4_6Microbiome and host physiology
  - LS4_7Nutrition and exercise physiology
  - LS4_8Impact of stress (including environmental stress) on physiology
  - LS4_9Metabolism and metabolic disorders, including diabetes and obesity
  - LS4_10The cardiovascular system and cardiovascular diseases
  - LS4_11Haematopoiesis and blood diseases
  - LS4_12Cancer
  - LS4_13Other non-communicable diseases (except disorders of the nervous system and immunity-related diseases)
- LS3Cell Biology, Development, Stem Cells and Regeneration
  - LS3_4Cell junctions, cell adhesion, the extracellular matrix, cell communication
  - LS3_5Cell signalling and signal transduction, exosome biology
  - LS3_6Organelle biology and trafficking
  - LS3_7Mechanobiology of cells, tissues and organs
  - LS3_8Embryogenesis, pattern formation, morphogenesis
  - LS3_9Cell differentiation, formation of tissues and organs
  - LS3_10Developmental genetics
  - LS3_11Evolution of developmental strategies
  - LS3_12Organoids
  - LS3_3Cell behaviour, including control of cell shape, cell migration
  - LS3_13Stem cells
  - LS3_14Regeneration
  - LS3_15Development of cell-based therapeutic approaches for tissue regeneration
  - LS3_17Theoretical modelling in cellular, developmental and regenerative biology
  - LS3_16Functional imaging of cells and tissues
  - LS3_1Cell cycle, cell division and growth
  - LS3_2Cell senescence, cell death, autophagy, cell ageing
- LS5Neuroscience and Disorders of the Nervous System
  - LS5_1Neuronal cells
  - LS5_3Neural development and related disorders
  - LS5_5Neural networks and plasticity
  - LS5_10Ageing of the nervous system
  - LS5_11Neurological and neurodegenerative disorders
  - LS5_12Mental disorders
  - LS5_7Sensory systems, sensation and perception, including pain
  - LS5_13Nervous system injuries and trauma, stroke
  - LS5_14Repair and regeneration of the nervous system
  - LS5_15Neuroimmunology, neuroinflammation
  - LS5_16Systems and computational neuroscience (e.g. modelling, simulation, brain oscillations, connectomics)
  - LS5_18Innovative methods and tools for neuroscience
  - LS5_17Imaging in neuroscience
  - LS5_9Neural basis of cognition (e.g. learning, memory, attention, emotions, speech)
  - LS5_6Neurovascular biology and blood-brain barrier
  - LS5_8Neural basis of behaviour (e.g. sleep, consciousness, addiction)
  - LS5_4Neural stem cells
  - LS5_2Glial cells and neuronal-glial communication
- LS6Immunity, Infection and Immunotherapy
  - LS6_1Innate immunity
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  - LS6_3Regulation of the immune response
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  - LS6_5Biology of pathogens (e.g. bacteria, viruses, parasites, fungi)
  - LS6_7Mechanisms of infection
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  - LS6_8Biological basis of prevention and treatment of infection
  - LS6_9Antimicrobials, antimicrobial resistance
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- LS8Environmental Biology, Ecology and Evolution
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  - LS8_15Theoretical developments and modelling in environmental biology, ecology, and evolution
- LS9Biotechnology and Biosystems Engineering
  - LS9_3Bioengineering of cells, tissues, organs and organisms
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  - LS9_4Microbial biotechnology and bioengineering
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  - LS9_6Marine biotechnology and bioengineering
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  - LS9_9Plant pathology and pest resistance
  - LS9_11Biomass production and utilisation, biofuels
  - LS9_12Ecotoxicology, biohazards and biosafety
  - LS9_1Bioengineering for synthetic and chemical biology
SHSocial Sciences and Humanities
- SH2Institutions, Governance and Legal Systems
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  - SH4_1Cognitive basis of human development, developmental disorders; comparative cognition
  - SH4_2Personality and social cognition; emotion
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  - SH6_1Archaeological methods and theory, history of archaeology
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