Semisymmetric Graphs of Order 2p^(3)with Valency p^(2)  

作　　者：Li Wang Songtao Guo Genghua Fan 

机构地区：[1]School of Mathematics and Information Science,Henan Polytechnic University Jiaozuo,Henan 454000,China [2]School of Mathematics and Statistics,Henan University of Science and Technology Luoyang,Henan 471023,China [3]不详

出　　处：《Algebra Colloquium》2024年第2期199-208,共10页代数集刊（英文版）

基　　金：partially supported by the Mathematical Tianyuan Foundation of China(11426093,12126317);National Natural Science Foundation of China(11501172,11301154);Natural Science Foundation of Henan Province,Fundamental Research Funds for the Universities of Henan Province(NSFRF240316);Young Core Teacher Foundation of Henan Polytechnic University(2023XQG-11).

摘　　要：A simple undirected regular graph is said to be semisymmetric if it is edge-transitive but not vertex-transitive.For a semisymmetric graphΓof order 2p^(3),p a prime,it is well known thatΓis bipartite with two biparts having equal size.The complete classification of such graphs has been given for the full automorphism group Aut(Γ)acting unfaithfully on at least one bipart ofΓ,which shows that there is only one infinite family of such graphs with valency p^(2).The graphs of this kind have been determined when Aut(Γ)acts faithfully and primitively on at least one bipart ofΓ,and thus there is only one remaining case for classifying such graphs of valency p^(2),Aut(Γ)acting faithfully and imprimitively on both biparts ofΓ,which is dealt with in this paper.As a result,there is only one infinite family of semisymmetric graphs of order 2p^(3)with valency p^(2).

关 键 词：semisymmetric graph semitransitive graph bi-coset graph 

分 类 号：O15[理学—数学]