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Keywords:
Weyl groups; root systems; girth of a graph
Weyl groups; root systems; girth of a graph
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.
References:
[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.
[2] Hulsurkar, S. G.: Proof of Verma’s conjecture on Weyl’s dimension polynomial. Investiones Math. 27 (1974), 45-52. MR 0369555 | Zbl 0298.17005
[3] Chastkofsky, L.: Variations on Hulsurkar’s matrix with applications to representations of Algebraic Chevalley groups. J. Algebra 82 (1983), 255-274. MR 0701046 | Zbl 0532.20023
[4] Bourbaki, N.: Groupes et algebres de Lie, Chap. IV-VI. Hermann, Paris, 1969.
[5] Humphreys, J. E.: Introduction to Lie Algebras and representation theory. Springer Verlag, New York, 1972. MR 0323842 | Zbl 0254.17004
[6] Hulsurkar S. G.: Non-planarity of graphs on Weyl groups. J. Math. Phy. Sci. 24 (1990), 363-367. MR 1087693 | Zbl 0732.05026
[7] Youssef, S. A., Hulsurkar, S. G.: Girth of a graph on Weyl groups. to appear in “Journal of Indian Academy of Mathematics".
[8] Harary, F.: Graph theory. Addison Wesley, Mass, 1972. MR 0256911
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