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 bipart...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).展开更多
基金partially supported by the Mathematical Tianyuan Foundation of China(11426093,12126317)National Natural Science Foundation of China(11501172,11301154)+1 种基金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).
文摘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).
