Tetravalent vertex-transitive graphs of order 4p

被引:8
作者
Zhou, Jin-Xin [1 ]
机构
[1] Beijing Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China
基金
中国国家自然科学基金;
关键词
Cayley graph; vertex-transitive graph; automorphism group; NON-CAYLEY GRAPHS; SYMMETRIC GRAPHS; PRIME; TWICE; AUTOMORPHISMS; VERTICES; PRODUCT; SQUARE; COVERS;
D O I
10.1002/jgt.20653
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A graph is vertex-transitive if its automorphism group acts transitively on vertices of the graph. A vertex-transitive graph is a Cayley graph if its automorphism group contains a subgroup acting regularly on its vertices. In this article, the tetravalent vertex-transitive non-Cayley graphs of order 4p are classified for each prime p. As a result, there are one sporadic and five infinite families of such graphs, of which the sporadic one has order 20, and one infinite family exists for every prime p>3, two families exist if and only if p=1 (mod 8) and the other two families exist if and only if p=1 (mod 4). For each family there is a unique graph for a given order.(C)2011 Wiley Periodicals, Inc.
引用
收藏
页码:402 / 415
页数:14
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