On connectedness of graphs on direct product of Weyl groups
Samy A. Youssef; S. G. Hulsurkar
Archivum Mathematicum (1995)
- Volume: 031, Issue: 4, page 299-304
- ISSN: 0044-8753
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topYoussef, Samy A., and Hulsurkar, S. G.. "On connectedness of graphs on direct product of Weyl groups." Archivum Mathematicum 031.4 (1995): 299-304. <http://eudml.org/doc/247684>.
@article{Youssef1995,
abstract = {In this paper, we have studied the connectedness of the graphs on the direct product of the Weyl groups. We have shown that the number of the connected components of the graph on the direct product of the Weyl groups is equal to the product of the numbers of the connected components of the graphs on the factors of the direct product. In particular, we show that the graph on the direct product of the Weyl groups is connected iff the graph on each factor of the direct product is connected.},
author = {Youssef, Samy A., Hulsurkar, S. G.},
journal = {Archivum Mathematicum},
keywords = {root systems; Weyl Groups; connectivity in a graph; Weyl groups; connectedness; graphs; connected components; direct products},
language = {eng},
number = {4},
pages = {299-304},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On connectedness of graphs on direct product of Weyl groups},
url = {http://eudml.org/doc/247684},
volume = {031},
year = {1995},
}
TY - JOUR
AU - Youssef, Samy A.
AU - Hulsurkar, S. G.
TI - On connectedness of graphs on direct product of Weyl groups
JO - Archivum Mathematicum
PY - 1995
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 031
IS - 4
SP - 299
EP - 304
AB - In this paper, we have studied the connectedness of the graphs on the direct product of the Weyl groups. We have shown that the number of the connected components of the graph on the direct product of the Weyl groups is equal to the product of the numbers of the connected components of the graphs on the factors of the direct product. In particular, we show that the graph on the direct product of the Weyl groups is connected iff the graph on each factor of the direct product is connected.
LA - eng
KW - root systems; Weyl Groups; connectivity in a graph; Weyl groups; connectedness; graphs; connected components; direct products
UR - http://eudml.org/doc/247684
ER -
References
top- Hulsurkar S.G., Nonplanarity of graphs on Weyl groups, J. Math. Phys. Sci., 24(1990) 363. (1990) MR1087693
- Hupmhreys J.E., Introduction to Lie Algebras and Representation theory, Springer-Verlag, New York, 1972. (1972) MR0323842
- Verma D.-N., Role of Affine Weyl Groups in the Representation Theory of Algebraic Chevalley Groups and their Lie Algebras, in “Lie Groups and their Representations", Ed. I.M.Gelfand, Halstead, New York, 1975. (1975) Zbl0316.20030MR0409673
- Hulsurkar S.G., Proof of Verma’s conjecture on Weyl’s dimension polynomial, Inventiones Math., 27(1974), 45. (1974) Zbl0298.17005MR0369555
- Narsingh Deo, Graph Theory, Prentice Hall of India, New Delhi, 1990. (1990)
- Youssef, Samy A., Hulsurkar S.G., On Connectedness of graphs on Weyl Groups of type , Arch. Math. (Brno) 31(1995), 163-170. (1995) MR1368255
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