More on the girth of graphs on Weyl groups

Samy A. Youssef; S. G. Hulsurkar

Archivum Mathematicum (1993)

  • Volume: 029, Issue: 1-2, page 19-23
  • ISSN: 0044-8753

Abstract

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The girth of graphs on Weyl groups, with no restriction on the associated root system, is determined. It is shown that the girth, when it is defined, is 3 except for at most four graphs for which it does not exceed 4.

How to cite

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Youssef, Samy A., and Hulsurkar, S. G.. "More on the girth of graphs on Weyl groups." Archivum Mathematicum 029.1-2 (1993): 19-23. <http://eudml.org/doc/247442>.

@article{Youssef1993,
abstract = {The girth of graphs on Weyl groups, with no restriction on the associated root system, is determined. It is shown that the girth, when it is defined, is 3 except for at most four graphs for which it does not exceed 4.},
author = {Youssef, Samy A., Hulsurkar, S. G.},
journal = {Archivum Mathematicum},
keywords = {Weyl groups; root systems; girth of a graph; girth; Weyl groups; root system},
language = {eng},
number = {1-2},
pages = {19-23},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {More on the girth of graphs on Weyl groups},
url = {http://eudml.org/doc/247442},
volume = {029},
year = {1993},
}

TY - JOUR
AU - Youssef, Samy A.
AU - Hulsurkar, S. G.
TI - More on the girth of graphs on Weyl groups
JO - Archivum Mathematicum
PY - 1993
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 029
IS - 1-2
SP - 19
EP - 23
AB - The girth of graphs on Weyl groups, with no restriction on the associated root system, is determined. It is shown that the girth, when it is defined, is 3 except for at most four graphs for which it does not exceed 4.
LA - eng
KW - Weyl groups; root systems; girth of a graph; girth; Weyl groups; root system
UR - http://eudml.org/doc/247442
ER -

References

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  1. The role of affine Weyl groups in the representation theory of algebraic groups and their Lie algebras. Lie Groups and their representations, Ed: I. M. Gelfand, John Wiley, New York, 1975. (1975) 
  2. Proof of Verma’s conjecture on Weyl’s dimension polynomial, Investiones Math. 27 (1974), 45-52. (1974) Zbl0298.17005MR0369555
  3. Variations on Hulsurkar’s matrix with applications to representations of Algebraic Chevalley groups, J. Algebra 82 (1983), 255-274. (1983) Zbl0532.20023MR0701046
  4. Groupes et algebres de Lie, Chap. IV-VI, Hermann, Paris, 1969. (1969) 
  5. Introduction to Lie Algebras and representation theory, Springer Verlag, New York, 1972. (1972) Zbl0254.17004MR0323842
  6. Non-planarity of graphs on Weyl groups, J. Math. Phy. Sci. 24 (1990), 363-367. (1990) Zbl0732.05026MR1087693
  7. Girth of a graph on Weyl groups, to appear in “Journal of Indian Academy of Mathematics". 
  8. Graph theory, Addison Wesley, Mass, 1972. (1972) MR0256911

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