A prime factor theorem for a generalized direct product

Wilfried Imrich; Peter F. Stadler

Discussiones Mathematicae Graph Theory (2006)

  • Volume: 26, Issue: 1, page 135-140
  • ISSN: 2083-5892

Abstract

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We introduce the concept of neighborhood systems as a generalization of directed, reflexive graphs and show that the prime factorization of neighborhood systems with respect to the the direct product is unique under the condition that they satisfy an appropriate notion of thinness.

How to cite

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Wilfried Imrich, and Peter F. Stadler. "A prime factor theorem for a generalized direct product." Discussiones Mathematicae Graph Theory 26.1 (2006): 135-140. <http://eudml.org/doc/270267>.

@article{WilfriedImrich2006,
abstract = {We introduce the concept of neighborhood systems as a generalization of directed, reflexive graphs and show that the prime factorization of neighborhood systems with respect to the the direct product is unique under the condition that they satisfy an appropriate notion of thinness.},
author = {Wilfried Imrich, Peter F. Stadler},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {products; set systems; prime factor theorem},
language = {eng},
number = {1},
pages = {135-140},
title = {A prime factor theorem for a generalized direct product},
url = {http://eudml.org/doc/270267},
volume = {26},
year = {2006},
}

TY - JOUR
AU - Wilfried Imrich
AU - Peter F. Stadler
TI - A prime factor theorem for a generalized direct product
JO - Discussiones Mathematicae Graph Theory
PY - 2006
VL - 26
IS - 1
SP - 135
EP - 140
AB - We introduce the concept of neighborhood systems as a generalization of directed, reflexive graphs and show that the prime factorization of neighborhood systems with respect to the the direct product is unique under the condition that they satisfy an appropriate notion of thinness.
LA - eng
KW - products; set systems; prime factor theorem
UR - http://eudml.org/doc/270267
ER -

References

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  1. [1] E. Cech, Topological spaces, Revised edition by Z. Frolí k and M. Katetov, Scientific editor, V. Pták. Editor of the English translation, Charles O. Junge (Publishing House of the Czechoslovak Academy of Sciences, Prague, 1966). Zbl0141.39401
  2. [2] W. Fontana and P. Schuster, Continuity in Evolution: On the Nature of Transitions, Science 280 (1998) 1451-1455, doi: 10.1126/science.280.5368.1451. 
  3. [3] P.C. Hammer, Extended topology: Continuity. I, Portugal. Math. 23 (1964) 77-93. Zbl0151.29302
  4. [4] W. Imrich and S. Klavžar, Product Graphs, Wiley-Interscience Series in Discrete Mathematics and Optimization, (Wiley-Interscience, New York, 2000) Structure and recognition, With a foreword by P. Winkler. 
  5. [5] R. McKenzie, Cardinal multiplication of structures with a reflexive relation, Fund. Math. 70 (1971) 59-101. Zbl0228.08002
  6. [6] B.M.R. Stadler and P.F. Stadler, Generalized topological spaces in evolutionary theory and combinatorial chemistry, J. Chem. Inf. Comput. Sci. 42 (2002) 577-585, doi: 10.1021/ci0100898. 
  7. [7] B.M.R. Stadler, P.F. Stadler, G. Wagner and W. Fontana, The topology of the possible: Formal spaces underlying patterns of evolutionary change, J. Theor. Biol. 213 (2001) 241-274, doi: 10.1006/jtbi.2001.2423. 
  8. [8] G. Wagner and P.F. Stadler, Quasi-independence, homology and the unity of type: A topological theory of characters, J. Theor. Biol. 220 (2003) 505-527, doi: 10.1006/jtbi.2003.3150. 

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