Some new results on the connected sum of certain digital surfaces
Downloads
DOI:
https://doi.org/10.26637/MJM0702/0027Abstract
In this paper, we construct some new digital surfaces from the topological sum of two digital surfaces. Also, we compute the digital simplicial homology groups of these digital surfaces. We calculate the Euler characteristics of certain digital connected surfaces. Moreover, we obtain some results of Euler characteristics of certain minimal simple closed surfaces.
Keywords:
Digital surface, simplicial homology groups, connected sum, Euler characteristicsMathematics Subject Classification:
Mathematics- Pages: 318-325
- Date Published: 01-04-2019
- Vol. 7 No. 02 (2019): Malaya Journal of Matematik (MJM)
H. Arslan, I. Karaca and A. Oztel, Homology groups of n-dimensional digital images, XXI-Turkish Natl. Math. Sympos., B (2008), 1-13.
G. Bertrand, Simple points, topological numbers and geodesic neighborhoods in cubic grids, Pattern Recogn. Lett., 15(1994), 1003-1011.
G. Bertrand and R. Malgouyres, Some topological properties of discrete surfaces, J. Math. Imaging Vis., 11(1999), 207-211.
L. Boxer, Digitally continuous functions, Pattern Recogn. Lett., 15(1994), 833-839.
L. Boxer, A classical construction for the digital fundamental group, J. Math. Imaging Vis., 10(1999), 51-62.
L. Boxer, Homotopy properties of sphere-like digital images, J. Math. Imaging Vis., 24(2006), 167-175.
L. Boxer, Digital products, wedges, and covering spaces, J. Math. Imaging Vis., 25(2006), 169-171.
L. Boxer, I. Karaca and A. Oztel, Topological invariant in digital images, J. Math. Sci. Adv. Appl., 11 (2011), 109140.
G. Burak and I. Karaca, Digital Borsuk-Ulam Theorem, Bull. Iranian Math. Soc., 43(2017), 477-499.
E. U. Demir, and I. Karaca, Simplicial homology groups of certain surfaces, Hacet. J. Math. Stat., 44(5)(2015), $1011-1022$.
E. U. Demir, and I. Karaca, An Algorithm for computing digital cohomology groups, App. Math. Inf. Sci., $10(3)(2016), 1017-1025$.
L. Chen, Discrete surfaces and manifolds, Sci. Prac. Comp., Rockville, MD(2004).
O. Ege and I. Karaca, Fundamental properties of digital simplicial homology groups, Amer. J. Comput. Technol. Appl., 1(2)(2013), 25-41.
O. Ege and I. Karaca, Cohomology theory for digital images, Rom. J. Inf. Sci. Technol., 16(1)(2013), 10-28.
O. Ege, I. Karaca, M. E. Ege, Relative homology groups of digital images, App. Math. Inf. Sci., 8(5)(2014), 23372345 .
O. Ege and I. Karaca, Digital cohomology operations, App. Math. Inf. Sci., 9(4)(2015), 1953-1960.
O. Ege, I. Karaca, Digital uniform spaces, Celal Bayar Uni. J. Sci., 12(2)(2016), 129-134.
O. Ege and I. Karaca, Some properties of digital $H$ spaces, Turkish J. Electr. Eng. Comput. Sci, 24(3)(2016), $1930-1941$
O. Ege and I. Karaca, Digital fibrations, Proc. Natl. Acad. Sci. India Sec. A., 87(1)(2017), 109-114..
S. E. Han, Connected sum of digital closed surfaces, Inf. Sci., $176(2006), 332-348$.
G. T. Herman, Oriented surfaces in digital spaces, CVGIP: Graph. Models Image Process, 55(1993), 381-396.
I. Karaca and G. Burak, Simplicial relative cohomology rings of digital images, App. Math. Inf. Sci., $8(5)(2014)$, $2375-2387$.
I. Karaca and I. Cinar, The cohomology structure of digital Khalimsky spaces, Rom. J. Math. Comput. Sci., $8(2018), 110-128$.
8 T. Y. Kong, A digital fundamental group, Comput. Graph., 13(1989), 159-166.
A. Rosenfeld, Digital topology, Amer. Math. Monthly, $86(1979), 76-87$
A. Rosenfeld, Continuous functions on digital pictures, Pattern Recogn. Lett., 4(1986), 177-184.
E. H. Spanier, Algebraic Topology. Springer-Verlag, New York(1966).
- NA
Similar Articles
- Ann Mary Philip, Sunny Joseph Kalayathankal , Joseph Varghese Kureethara, On different kinds of arcs in interval valued fuzzy graphs , Malaya Journal of Matematik: Vol. 7 No. 02 (2019): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2019 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
