Pinwheel tiling fractal graph- a notion to edge cordial and cordial labeling

 
 
 
  • Abstract
  • Keywords
  • References
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  • Abstract


    A fractal is a complex geometric figure that continues to display self-similarity when viewed on all scales. Tile substitution is the process of repeatedly subdividing shapes according to certain rules. These rules are also sometimes referred to as inflation and deflation rule. One notable example of a substitution tiling is the so-called Pinwheel tiling of the plane. Many examples of self-similar tiling are made of fractiles: tiles with fractal boundaries. . The pinwheel tiling was the first example of this sort. There are many as such as family of tiling fractal curves, but for my study, I have considered this Pinwheel and its two intriguing Pinwheel properties of tiling fractals. These fractals have been considered as a graph and the same has been viewed under the scope of cordial and edge cordial labeling to apply this concept for further study in Engineering and science applications.


  • Keywords


    Pinwheel Tiling; Fractals; Graph Labeling; Cordial and Edge Cordial.

  • References


      [1] Bloom G. S. and Golomb S. W. (1977). Applications of numbered undirected graphs, Proc of IEEE, 65(4), 562-570. http://dx.doi.org/10.1109/PROC.1977.10517.

      [2] Cahit I. (1987). Cordial Graphs: A weaker version of graceful and harmonious Graphs, Ars Combinatoria, 23,201-207.

      [3] Charlen radin (2014), the pinwheel tiling of the plane, Annals of mathematics, 139(1999), 661-702. http://dx.doi.org/10.2307/2118575.

      [4] DIRK FRETTL¨OH, (et. al.), COHOMOLOGY OF THE PINWHEEL TILING, J. Aust. Math. Soc. 97 162—179 http://dx.doi.org/10.1017/S1446788714000275.

      [5] Gallian, J. A. (2009). A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, 16, #DS 6.

      [6] Harary, F. (1972). Graph Theory, Massachusetts, Addison Wesley.

      [7] James Gleick (1998), Chaos, Vintage Publishers.

      [8] Karzes, T. Tiling Fractal curves published online at: http://karzes.best.vwh.net.

      [9] M. Barnsley (1988), Fractals Everywhere, Academic Press Inc.,

      [10] M. Baake, D. Frettlo¨ h, and U. Grimm, (2007), Pinwheel patterns and powder diffraction, Phil. Mag. 87, 2831–2838. http://dx.doi.org/10.1080/14786430601057953.

      [11] M. Seoud and A. E. I. Abdel Maqsoud (1999) “On cordial and balanced labeling of graphs”, Journal of Egyptian Math. Soc., Vol. 7, pp. 127-135.

      [12] Natalie Priebe Frank, Michael Whittaker (2010), A Fractal Version of the Pinwheel Tiling, THE MATHEMATICAL INTELLIGENCER.

      [13] R. Devaney and L. Keen, eds.( 1989 ), Chaos and Fractals: The Mathematics Behind the Computer Graphics, American Mathematical Society, Providence http://dx.doi.org/10.1090/psapm/039.

      [14] RI, Robin Wilson (2013), Non-periodic tiling in blender, c.g space. Blogger.

      [15] Sathakathulla A.A. (2014), Ter- dragon curve: a view in cordial and edge cordial labeling, International Journal of Applied Mathematical Research, 3 (4) 454-457. http://dx.doi.org/10.14419/ijamr.v3i4.3426.

      [16] Simon Parzer (2013), Irrational Image Generator, MASTER’S THESIS, Vienna University of Technology,

      [17] Sundaram M., Ponraj R. and Somasundram S. (2005). Prime Cordial Labeling of graphs, J.Indian Acad. Math., 27 (2), 373-390.


 

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Article ID: 5700
 
DOI: 10.14419/ijamr.v5i2.5700




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