Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero 3-flow. In this paper, we show that this conjecture is true for Cayley graph on generalized dihedral groups and generalized quaternion groups, ...Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero 3-flow. In this paper, we show that this conjecture is true for Cayley graph on generalized dihedral groups and generalized quaternion groups, which generalizes the result of F. Yang and X. Li [Inform. Process. Lett., 2011, 111： 416-419]. We also generalizes an early result of M. Nanasiova and M. Skoviera [J. Algebraic Combin., 2009, 30： 103-110].展开更多
Abstract Denote by Qm the generalized quaternion group of order 4m. Let R（Qm） be its complex representation ring, and △（Qm） its augmentation ideal. In this paper, the author gives an explicit Z-basis for the △n...Abstract Denote by Qm the generalized quaternion group of order 4m. Let R（Qm） be its complex representation ring, and △（Qm） its augmentation ideal. In this paper, the author gives an explicit Z-basis for the △n（Qm） mid determines the isomorphism class of the n-th augmentation quotient for each positive integer n.展开更多
基金Acknowledgements The first author was supported by the Natural Science Foundation of China （Grant No. 11301254）, the Natural Science Foundation of Henan Province （Grant No. 132300410313）, and the Natural Science Foundation of Education Bureau of Henan Province （Grant No. 13A110800）. The second author was supported by the National Natural Science Foundation of China （Grant No. 11171129） and the Doctoral Fund of Ministry of Education of China （Grant No. 20130144110001）.
文摘Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero 3-flow. In this paper, we show that this conjecture is true for Cayley graph on generalized dihedral groups and generalized quaternion groups, which generalizes the result of F. Yang and X. Li [Inform. Process. Lett., 2011, 111： 416-419]. We also generalizes an early result of M. Nanasiova and M. Skoviera [J. Algebraic Combin., 2009, 30： 103-110].
基金supported by the National Natural Science Foundation of China(Nos.11226066,11401155)Anhui Provincial Natural Science Foundation(No.1308085QA01)
文摘Abstract Denote by Qm the generalized quaternion group of order 4m. Let R（Qm） be its complex representation ring, and △（Qm） its augmentation ideal. In this paper, the author gives an explicit Z-basis for the △n（Qm） mid determines the isomorphism class of the n-th augmentation quotient for each positive integer n.
