至多有150个点的3度非对称的点传递图
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摘要
设X为3度连通的简单无向图，X称为具有非平凡点稳定子群的非对称
的点传递图，若X的全自同构群A在X的顶点集合上作用是传递的，而且
X的任意顶点在A中的稳定子群在该点的邻域上的作用是非传递的、非平
凡的。本文考察了这种图，即当限制其顶点数不超过150且基本圈长度为素
数时，给出了这些图的一个描述。
Trivalent Nonsymmetric Vertex-Transitive Graphs Of Order At
Most 150
Ma XueSong
Dept. of Math.,Capital Normal University,Beijing 100037
Abstract
Let X be a finite simple undirect connected trivalent graph. X is said to be a
nonsymmetric vertex-transitive graph with a nontrivial vertex-stabilizer if the full au-
tomorphism group of X acts transitively on the vertex set of X and the vertex-stabilizer
in it of a vertex u is neither transitive nor trivial on the set of vertices adjacent to
the vertex v. In this paper, for the above-mentioned graphs of order at most 150 and
with the basic cycles of prime length, we give a description.
的点传递图，若X的全自同构群A在X的顶点集合上作用是传递的，而且
X的任意顶点在A中的稳定子群在该点的邻域上的作用是非传递的、非平
凡的。本文考察了这种图，即当限制其顶点数不超过150且基本圈长度为素
数时，给出了这些图的一个描述。
Trivalent Nonsymmetric Vertex-Transitive Graphs Of Order At
Most 150
Ma XueSong
Dept. of Math.,Capital Normal University,Beijing 100037
Abstract
Let X be a finite simple undirect connected trivalent graph. X is said to be a
nonsymmetric vertex-transitive graph with a nontrivial vertex-stabilizer if the full au-
tomorphism group of X acts transitively on the vertex set of X and the vertex-stabilizer
in it of a vertex u is neither transitive nor trivial on the set of vertices adjacent to
the vertex v. In this paper, for the above-mentioned graphs of order at most 150 and
with the basic cycles of prime length, we give a description.
引文
[1] J.A.Bondy and U.S.R Murty .Graph Theory with Applications. Macmillan Press, London 1977．
[2] N. Biggs, Algebraic Graph Theory (the 2nd edition), Cambriage University Press, 1993．
[3] Ying Chang and James Oxley, On Weakly Symmetric Graphs of Order Twice a Prime, J. Combin. Theory. Ser.B 42． 196-211(1987) .
[4] H.S.M. Coxeter and W.O.Moser, Gennerators and Relations for Discrete Groups, (the second edition). Springer-Verlag, Berlin, 1965．
[5] H.S.M Coxetar Robert Frucht and David L. Powers, Zero-symmetric graphs, Academic Press Now York 1981．
[6] B. Huppert, 'Endliche Gruppen I,' Spring-Verlag, New York Berlin, 1967．
[7] B. Huppert, 'Endliche Gruppen 11, ' Spring-Verlag, New York Berlin, 1967．
[8] M. Hall, Jr. Construction Of Finite Simple Groups, Computers In Algebra And Number Theory, SIAN-AMS, Proceedings, American Mathematical Society (1971) pp. 109-134．
[9] Pater Lorimer, Vertex-Transitive Graphs Of Valency 3, Europ. J. Combinatorics (1983) 4 37-44．
[10] Peter Lorimer, Trivalent Symmetric Graphs Of Order At Most 120, Europ. J. Combin. (1984) 5． 163-171．
[11] Peter Lorimer, Vertex-transitive Graphs, Particulary Symmetric Graphs of prime Valency, J. Graph Theory Vol. 8． (1984) 55-68．
[12] Dian-Jun Wang, The Automorphism Groups Of Vertex-Transitive Cubic Graphs, (Peking University Ph. D. Thesis 1997) .
[13] H. Wielandt, 'Finite Permutation Groups', Academic Press, New York, 1964．
[14] Ming-Yao Xu, The Introduction of Finite Group', Science Press, BeiJing, 1995． Trivalent Nonsymmetric Vertex-Transitive Graphs Of Order At Most 150 Ma XueSong Dept. of Math.,Capital Normal University,Beijing 100037
[2] N. Biggs, Algebraic Graph Theory (the 2nd edition), Cambriage University Press, 1993．
[3] Ying Chang and James Oxley, On Weakly Symmetric Graphs of Order Twice a Prime, J. Combin. Theory. Ser.B 42． 196-211(1987) .
[4] H.S.M. Coxeter and W.O.Moser, Gennerators and Relations for Discrete Groups, (the second edition). Springer-Verlag, Berlin, 1965．
[5] H.S.M Coxetar Robert Frucht and David L. Powers, Zero-symmetric graphs, Academic Press Now York 1981．
[6] B. Huppert, 'Endliche Gruppen I,' Spring-Verlag, New York Berlin, 1967．
[7] B. Huppert, 'Endliche Gruppen 11, ' Spring-Verlag, New York Berlin, 1967．
[8] M. Hall, Jr. Construction Of Finite Simple Groups, Computers In Algebra And Number Theory, SIAN-AMS, Proceedings, American Mathematical Society (1971) pp. 109-134．
[9] Pater Lorimer, Vertex-Transitive Graphs Of Valency 3, Europ. J. Combinatorics (1983) 4 37-44．
[10] Peter Lorimer, Trivalent Symmetric Graphs Of Order At Most 120, Europ. J. Combin. (1984) 5． 163-171．
[11] Peter Lorimer, Vertex-transitive Graphs, Particulary Symmetric Graphs of prime Valency, J. Graph Theory Vol. 8． (1984) 55-68．
[12] Dian-Jun Wang, The Automorphism Groups Of Vertex-Transitive Cubic Graphs, (Peking University Ph. D. Thesis 1997) .
[13] H. Wielandt, 'Finite Permutation Groups', Academic Press, New York, 1964．
[14] Ming-Yao Xu, The Introduction of Finite Group', Science Press, BeiJing, 1995． Trivalent Nonsymmetric Vertex-Transitive Graphs Of Order At Most 150 Ma XueSong Dept. of Math.,Capital Normal University,Beijing 100037