Topological complexities of finite digital images

Subject Areas : Algebraic topology

M. Is ¹ , I. Karaca ²

1 - Department of Mathematics, Faculty of Science, Ege University, Izmir, Turkey
2 - Department of Mathematics, Faculty of Science, Ege University, Izmir, Turkey

Received: 2022-02-12 Accepted : 2022-03-30 Published : 2022-03-30

Keywords:

References:

[1] C. Berge. Graphs and Hypergraphs, 2nd edition, Amsterdam, Netherlands, 1973.

[2] A. Borat. T, Vergili, Digital Lusternik-Schnirelmann category, Turk. J. Math. 42 (2018), 1845-1852.

[3] L. Boxer, A classical construction for the digital fundamental group, J. Math. Imaging Vis. 10 (1999), 51-62.

[4] L. Boxer, Digitally continuous functions, Pattern Recognit. Lett. 15 (1994), 833-839.

[5] L. Boxer, Digital products, wedges, and covering spaces, J. Math. Imaging Vis. 25 (2006), 169-171.

[6] L. Boxer, Fixed point sets in digital topology 2, Appl. Gen. Topol. 21 (1) (2020), 111-133.

[7] L. Boxer, Homotopy properties of sphere-like digital images, J. Math. Imaging Vis. 24 (2006), 167-175.

[8] L. Boxer, Properties of digital homotopy, J. Math. Imaging Vis. 22 (2005), 19-26.

[9] L. Boxer, I. Karaca, Fundamental groups for digital products, Adv. Appl. Math. Sci. 11 (4) (2012) 161-180.

[10] L. Boxer, P. C. Staecker, Fixed point sets in digital topology 1, Appl. Gen. Topol. 21 (1) (2020), 87-110.

[11] L. Chen, Discrete Surfaces and Manifolds: A Theory of Digital-Discrete Geometry and Topology, Scientific & Practical Computing, 2004.

[12] L. Chen, Y. Rong, Digital topological method for computing genus and the Betti numbers, Topol. Appl. 157 (12) (2010), 1931-1936.

[13] O. Ege, I. Karaca, Cohomology theory for digital images, Rom. J. Inf. Sci. Tech. 16 (1) (2013), 10-28.

[14] O. Ege, I. Karaca, M. E. Ege, Relative homology groups in digital images, Appl. Math. Inf. Sci. 8 (5) (2014), 2337-2345.

[15] M. Farber, Topological complexity of motion planning, Discrete Comput. Geom. 29 (2003), 211-221.

[16] M. Farber, Invitation to Topological Robotics, European Mathematical Society, 2008.

[17] J. Haarman, M. P. Murphy, C. S. Peters, P. C. Staecker, Homotopy equivalence in finite digital images, J. Math. Imaging Vis. 53 (2015), 288-302.

[18] G. T. Herman, Oriented surfaces in digital spaces, CVGIP-Graph Model Im. 55 (1993), 381-396.

[19] M. Is, I. Karaca, The higher topological complexity in digital images, Appl. Gen. Topol. 21 (2020), 305-325.

[20] I. Karaca, M. Is, Digital topological complexity numbers, Turk. J. Math. 42 (6) 2018, 3173-3181.

[21] E. Khalimsky, Motion, Deformation, and Homotopy in Finite Spaces, Proceedings IEEE International Conference on Systems, Man and Cybernetics, 1987.

[22] T. Y. Kong, A digital fundamental group, Comput. Graph. 13 (1989), 159-166.

[23] D. G. Morgenthaler, A. Rosenfeld, Surfaces in three-dimensional images, Inf. Control. 51 (1981), 227-247.

[24] A. Rosenfeld, Connectivity in digital pictures, J. ACM. 17 (1970), 146-160.

[25] A. Rosenfeld, Digital topology, Am. Math. Mon. 86 (1979), 76-87.

[26] Y. Rudyak, On higher analogs of topological complexity, Topol. Appl. 157 (5) (2010), 916-920.