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Structural Analysis of Complex Networks pp 335–356Cite as

A Chromatic Metric on Graphs

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Abstract

In this chapter, we introduce the concept of relatedness of graphs, based upon the generalized chromatic number. This allows the definition of a graph metric. It is proved that the distance between any two graphs is at most three.

MSC2000: Primary 05C12; Secondary 05C15

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References

  1. Benadé JG (1990) Some aspects of generalised graph colourings. Ph.D thesis, Department of Mathematics, Rand Afrikaans University

    Google Scholar 

  2. Benadé G, Broere I (1988) Generalized colourings: existence of uniquely colourable graphs. Verslagreeks van die Departement Wiskunde, RAU, no. 6/88

    Google Scholar 

  3. Benadé G, Broere I (1990) A construction of uniquely C 4-free colourable graphs. Quaest Math 13:259–264

    Article  MATH  Google Scholar 

  4. Benadé G, Broere I (1992) Chromatic relatedness of graphs. Ars Combinatoria 34:326–330

    MATH  MathSciNet  Google Scholar 

  5. Bollobás B, Thomason AG (1977) Uniquely partitionable graphs. J Lond Math Soc 16: 403–410

    Article  MATH  Google Scholar 

  6. Broere I, Frick M (1988) A characterization of the sequence of generalized chromatic numbers of a graph. In: Proceedings of the 6th international conference on the theory and applications of graphs, Kalamazoo

    Google Scholar 

  7. Broere I, Frick M (1990) On the order of uniquely colourable graphs. Discrete Math 82(3): 225–232

    Article  MATH  MathSciNet  Google Scholar 

  8. Brown JI (1987) A theory of generalized graph colouring. Ph.D. thesis, Department of Mathematics, University of Toronto

    Google Scholar 

  9. Brown JI, Corneil DG (1987) On generalized graph colourings. J Graph Theory 11:87–99

    Article  MATH  MathSciNet  Google Scholar 

  10. Burger M (1984) The cochromatic number of a graph. Ph.D. thesis, Department of Mathematics, Rand Afrikaans University

    Google Scholar 

  11. Chartrand G, Geller DP (1968) On uniquely colorable planar graphs. J Combin Theory 6: 265–271

    Google Scholar 

  12. Chartrand G, Lesniak L (1986) Graphs and digraphs, 2nd edn. Wadsworth, Belmont

    MATH  Google Scholar 

  13. Folkman J (1970) Graphs with monochromatic complete subgraphs in every edge colouring. SIAM J Appl Math 18:19–24

    Article  MATH  MathSciNet  Google Scholar 

  14. Frick M (1987) Generalised colourings of graphs. Ph.D thesis, Department of Mathematics, Rand Afrikaans University

    Google Scholar 

  15. Greenwell D, Lovász L (1974) Applications of product colouring. Acta Math Acad Sci H 25:335–340

    Article  MATH  Google Scholar 

  16. Harary F (1985) Conditional colorablility of graphs. In: Harary F, Maybee J (eds) Graphs and applications. Proc 1st Col Symp Graph theory. Wiley, New York, pp 127–136

    Google Scholar 

  17. Lesniak-Foster L, Straight HJ (1977) The cochromatic number of a graph. Ars Combinatoria 3:39–45

    MATH  MathSciNet  Google Scholar 

  18. Mynhardt CM, Broere I (1985) Generalized colorings of graphs. In: Alavi Y et al (eds) Graph theory and its applications to algorithms and computer science. Wiley, New York, pp 583–594

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Computer Science, Statistics and Mathematics, North-West University, Potchefstroom, South Africa

    Gerhard Benadé

Authors
  1. Gerhard Benadé
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Correspondence to Gerhard Benadé .

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Editors and Affiliations

  1. Medizinische Informatik und Technik, Institute for Bioinformatics and Transla, UMIT-Private Universität für Gesundheits, Eduard Wallnöfer-Zentrum 1, Hall in Tirol, A-6060, Austria

    Matthias Dehmer

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Benadé, G. (2011). A Chromatic Metric on Graphs. In: Dehmer, M. (eds) Structural Analysis of Complex Networks. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4789-6_13

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