JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Enumerations of Finite Topologies Associated with a Finite Simple Graph
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 54, Issue 4,  2014, pp.655-665
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2014.54.4.655
 Title & Authors
Enumerations of Finite Topologies Associated with a Finite Simple Graph
Kim, Dongseok; Kwon, Young Soo; Lee, Jaeun;
  PDF(new window)
 Abstract
The number of topologies (non-homeomorphic topologies) on a fixed finite set having n elements are now known up to n = 18 (n = 16 respectively) but still no complete formula yet. There are one to one correspondences among topologies, preorders and transitive digraphs on a given finite set. In this article, we enumerate topologies and non-homeomorphic topologies whose underlying graph is a given finite simple graph.
 Keywords
finite topology;preorder;graph;
 Language
English
 Cited by
 References
1.
L. W. Brinn, Computing topologies, Mathematics Magazine, 58(1985), 67-77. crossref(new window)

2.
J. W. Evans, F. Harary and M. S. Lynn, On the computer enumeration of finite topologies, Communications of the ACM, 10(1967), 295-297. crossref(new window)

3.
J. Gross and T. Tucker, Topological graph theory, Wiley-Interscience Series in discrete Mathematics and Optimization, Wiley & Sons, New York, 1987.

4.
V. A. Kovalevsky, Finite topology as applied to image analysis, Computer Vision, Graphics, and Image Processing, 46(1989), 141-161. crossref(new window)

5.
V. A. Kovalevsky, Finite topology and image analysis, Advances in electronics and electron physics, 84(1992), 197-324. crossref(new window)

6.
C. Marijuan, Finite topology and digraphs, Proyecciones Journal of Mathematics, 29(2010), 291-307.

7.
R. Merrifield and H. Simmons, The structures of molecular topological spaces, Theoretica Chimica Acta, 55(1980), 55-75. crossref(new window)

8.
R. Merrifield and H. Simmons, Topological methods in chemistry, Wiley, New York, 1989.

9.
K. Ragnarsson and B. E. Tenner, Obtainable sizes of topologies on finite sets, Journal of Combinatorial Theory, Series A, 117(2010), 138-151, arXiv:0802.2550 crossref(new window)

10.
A. Rosenfeld, T. Kong and A. Wu, Digital surfaces, Graphical Models and Image Processing, 53(1991), 305-312. crossref(new window)

11.
N. J. A. Sloane, On-Line Encyclopedia of Integer Sequences, A000798, A001035, A001930, A000112. Available at http://oeis.org/.

12.
J. R. Stallings, Topology of finite graphs, Invent. math., 71(1983), 551-565. crossref(new window)

13.
T. Van Zandt. PSTricks: PostScript macros for generic TEX. Available at ftp://ftp.princeton.edu/pub/tvz/.