| Title:
|
More on the girth of graphs on Weyl groups (English) |
| Author:
|
Youssef, Samy A. |
| Author:
|
Hulsurkar, S. G. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
29 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
19-23 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Weyl groups |
| Keyword:
|
root systems |
| Keyword:
|
girth of a graph |
| MSC:
|
05C25 |
| MSC:
|
05C38 |
| MSC:
|
20F55 |
| idZBL:
|
Zbl 0798.05029 |
| idMR:
|
MR1242624 |
| . |
| Date available:
|
2008-06-06T21:23:33Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107462 |
| . |
| Reference:
|
[1] Verma, D. N.: 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. |
| Reference:
|
[2] Hulsurkar, S. G.: Proof of Verma’s conjecture on Weyl’s dimension polynomial.Investiones Math. 27 (1974), 45-52. Zbl 0298.17005, MR 0369555 |
| Reference:
|
[3] Chastkofsky, L.: Variations on Hulsurkar’s matrix with applications to representations of Algebraic Chevalley groups.J. Algebra 82 (1983), 255-274. Zbl 0532.20023, MR 0701046 |
| Reference:
|
[4] Bourbaki, N.: Groupes et algebres de Lie, Chap. IV-VI.Hermann, Paris, 1969. |
| Reference:
|
[5] Humphreys, J. E.: Introduction to Lie Algebras and representation theory.Springer Verlag, New York, 1972. Zbl 0254.17004, MR 0323842 |
| Reference:
|
[6] Hulsurkar S. G.: Non-planarity of graphs on Weyl groups.J. Math. Phy. Sci. 24 (1990), 363-367. Zbl 0732.05026, MR 1087693 |
| Reference:
|
[7] Youssef, S. A., Hulsurkar, S. G.: Girth of a graph on Weyl groups.to appear in “Journal of Indian Academy of Mathematics". |
| Reference:
|
[8] Harary, F.: Graph theory.Addison Wesley, Mass, 1972. MR 0256911 |
| . |
