DOI QR코드

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AN EQUIVALENT PROPERTY OF A NORMAL ADJACENCY OF A DIGITAL PRODUCT

  • Han, Sang-Eon (Faculty of Liberal Education, Institute of Pure and Applied Mathematics, Chonbuk National University)
  • 투고 : 2014.01.17
  • 심사 : 2014.02.05
  • 발행 : 2014.03.25

초록

Owing to the development of the notion of normal adjacency of a digital product [9], product properties of digital topological properties were studied efficiently. To equivalently represent a normal adjacency of a digital product, the present paper proposes an S-compatible adjacency of a digital product. This approach can be helpful to understand a normal adjacency of a digital product. Finally, using an S-compatible adjacency of a digital product, we can study product properties of digital topological properties, which improves the presentations of the normal adjacency of a digital product in [9] and [5, 6].

키워드

참고문헌

  1. C. Berge, Graphs and Hypergraphs, 2nd ed., North-Holland, Amsterdam, 1976.
  2. G. Bertrand, Simple points, topological numbers and geodesic neighborhoods in cubic grids, Pattern Recognition Letters 15 (1994), 1003-1011. https://doi.org/10.1016/0167-8655(94)90032-9
  3. G. Bertrand and R. Malgouyres, Some topological properties of discrete surfaces, Jour. of Mathematical Imaging and Vision 20 (1999), 207-221.
  4. L. Boxer, A classical construction for the digital fundamental group, Jour. of Mathematical Imaging and Vision 10 (1999), 51-62. https://doi.org/10.1023/A:1008370600456
  5. L. Boxer, Digital Products, Wedge; and Covering Spaces, Jour. of Mathematical Imaging and Vision 25 (2006), 159-171. https://doi.org/10.1007/s10851-006-9698-5
  6. L. Boxer and I. Karaca, Fundamental groups for digital products, Advances and Applications in Mathematical Sciences 11(4) (2012), 161-179.
  7. L. Chen, Discrete Surfaces and Manifolds: A Theory of Digital Discrete Geometry and Topology, Scientific and Practical Computing, Rockville, 2004.
  8. S.E. Han, Digital coverings and their applications, Jour. of Applied Mathematics and Computing 18(1-2) (2005), 487-495.
  9. S.E. Han, Non-product property of the digital fundamental group, Information Sciences 171(1-3) (2005), 73-91. https://doi.org/10.1016/j.ins.2004.03.018
  10. S.E. Han, On the simplicial complex stemmed from a digital graph, Honam Mathematical Journal 27(1) (2005), 115-129 .
  11. S.E. Han, Discrete Homotopy of a Closed k-Surface LNCS 4040, Springer-Verlag, Berlin, pp.214-225 (2006).
  12. S.E. Han, Erratum to "Non-product property of the digital fundamental group", Information Sciences 176(1) (2006), 215-216. https://doi.org/10.1016/j.ins.2005.03.014
  13. S.E. Han, Minimal simple closed 18-surfaces and a topological preservation of 3D surfaces, Information Sciences 176(2) (2006), 120-134. https://doi.org/10.1016/j.ins.2005.01.002
  14. S.E. Han, Strong k-deformation retract and its applications, Journal of the Korean Mathematical Society 44(6) (2007), 1479-1503. https://doi.org/10.4134/JKMS.2007.44.6.1479
  15. S.E. Han, Equivalent ($k_0$, $k_1$)-covering and generalized digital lifting, Information Sciences 178(2) (2008), 550-561. https://doi.org/10.1016/j.ins.2007.02.004
  16. S.E. Han, The k-homotopic thinning and a torus-like digital image in $Z^n$, Journal of Mathematical Imaging and Vision 31(1) (2008), 1-16. https://doi.org/10.1007/s10851-007-0061-2
  17. S.E. Han, Cartesian product of the universal covering property, Acta Applicandae Mathematicae 108 (2010), 363-383.
  18. S.E. Han, KD-($k_0$, $k_1$)-homotopy equivalence and its applications, Journal of Korean Mathematical Society 47(5) (2010), 1031-1054. https://doi.org/10.4134/JKMS.2010.47.5.1031
  19. S.E. Han, Multiplicative property of the digital fundamental group, Acta Applicandae Mathematicae 110(2) (2010), 921-944. https://doi.org/10.1007/s10440-009-9486-5
  20. S.E. Han, Ultra regular covering space and its automorphism group, International Journal of Applied Mathematics & Computer Science, 20(4) (2010), 699-710.
  21. S.E. Han, Non-ultra regular digital covering spaces with nontrivial automorphism groups, Filomat, 27(7) (2013), 1205-1218. https://doi.org/10.2298/FIL1307205H
  22. S.E. Han and Sik Lee, Remarks on digital products with normal adjacency relations, Honam Mathematical Journal 35(3) (2013), 515-524. https://doi.org/10.5831/HMJ.2013.35.3.515
  23. S.E. Han and B.G. Park, Digital graph ($k_0$, $k_1$)-homotopy equivalence and its applications, http://atlas-conferences.com/c/a/k/b/35.htm (2003).
  24. F. Harary, Graph theory, Addison-Wesley Publishing, Reading, MA, 1969.
  25. G. T. Herman, Geometry of Digital Spaces Birkhauser, Boston, 1998.
  26. E. Khalimsky, Motion, deformation, and homotopy in finite spaces, Proceedings IEEE International Conferences on Systems, Man, and Cybernetics (1987), 227-234.
  27. T.Y. Kong, A. Rosenfeld, Topological Algorithms for the Digital Image Processing, Elsevier Science, Amsterdam, 1996.
  28. W.S. Massey, Algebraic Topology, Springer-Verlag, New York, 1977.
  29. B.G. Park and S.E. Han, Classification of of digital graphs vian a digital graph ($k_0$, $k_1$)-isomorphism, http://atlas-conferences.com/c/a/k/b/36.htm (2003).
  30. A. Rosenfeld, Digital topology, Am. Math. Mon. 86 (1979), 76-87.
  31. A. Rosenfeld and R. Klette, Digital geometry, Information Sciences 148 (2003), 123-127 .
  32. E.H. Spanier, Algebraic Topology, McGraw-Hill Inc., New York, 1966.

피인용 문헌

  1. COMPARISON AMONG SEVERAL ADJACENCY PROPERTIES FOR A DIGITAL PRODUCT vol.37, pp.1, 2015, https://doi.org/10.5831/HMJ.2015.37.1.135
  2. REMARKS ON HOMOTOPIES ASSOCIATED WITH KHALIMSKY TOPOLOGY vol.37, pp.4, 2015, https://doi.org/10.5831/HMJ.2015.37.4.577
  3. UTILITY OF DIGITAL COVERING THEORY vol.36, pp.3, 2014, https://doi.org/10.5831/HMJ.2014.36.3.695