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Distance-Regular Graphs of Diameter 3Without Triangles with c_(2)=2

Communications in Mathematics and Statistics 2022年第4期10卷 785-792页

作者： a.a.makhnev Wenbin Guo K.S.Efimov Department of Mathematics Hainan UniversityHaikou 570228HainanPeople’s Republic of China Institute of Mathematics and Mechanics Ural Branch of the Russian Academy of SciencesYekaterinburgRussia University of Science and Technology of China Hefei 230026People’s Republic of China Ural Federal University named after the First President of Russia B.N.Yeltsin YekaterinburgRussia

Earlier it was proved that some distance-regular graphs of diameter 3 with c_(2)=2 do not ***-regular graphΓwith intersection array{17,16,10;1,2,8}has strongly regular graphΓ_(3)(pseudo-geometric graph for the net pG_(9)(17,9)).By symmetrizing the arrays of triple intersection numbers,it is proved that the distanceregular graphs with intersection arrays{17,16,10;1,2,8}and{22,21,4;1,2,14}do not exist.

关键词： Distance-regular graph Graph without triangles Triple intersection numbers

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Inverse Problems in Graph Theory: Nets

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Communications in Mathematics and Statistics 2019年第1期7卷 69-83页

作者： a.a.makhnev M.P.Golubyatnikov Wenbin Guo Institute of Mathematics and Mechanics Ural Branch of the Russian Academy of SciencesYekaterinburgRussia Ural Federal University named after the First President of Russia B.N.Yeltsin YekaterinburgRussia University of Science and Technology of China HefeiChina

Let Г be a distance-regular graph of diameter 3 with strong regular graph Г_(3).The determination of the parameters Г_(3) over the intersection array of the graph Г is a direct *** an intersection array of the graph Г with respect to the parameters Г_(3) is an inverse ***,inverse problemswere solved for Г_(3) by makhnev and *** this paper,we study the intersection arrays of distance-regular graph Г of diameter 3,for which the graph Г_(3) is a pseudo-geometric graph of the net PGm(n,m).New infinite series of admissible intersection arrays for these graphs are *** also investigate the automorphisms of distance-regular graph with the intersection array{20,16,5;1,1,16}.

关键词： Distance-regular graph Pseudo-geometric graph Strong regular graph

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On Automorphisms of Distance-Regular Graph with Intersection Array{18,15,9;1,1,10}

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Communications in Mathematics and Statistics 2015年第4期3卷 527-534页

作者： a.a.makhnev D.V.Paduchikh Institute of Mathematics and Mechanics UB RAS YekaterinburgRussian Federation

Recently,makhnev and Nirova found intersection arrays of distance-regular graphs withλ=2 and at most 4096 *** the case of primitive graphs of diameter 3 withμ=1 there corresponding arrays are{18,15,9;1,1,10},{33,30,8;1,1,30}or{39,36,4;1,1,36}.In this work,possible orders and subgraphs of fixed points of the hypothetical distance-regular graph with intersection array{18,15,9;1,1,10}are *** particular,graph with intersection array{18,15,9;1,1,10}is not vertex symmetric.

关键词： Distance-regular graph Automorphism Vertex symmetric graph

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On Nearly SS-Embedded Subgroups of Finite Groups

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Chinese Annals of Mathematics,Series B 2014年第6期35卷 885-894页

作者： Lijun HUO Wenbin GUO Alexander A.makhnev Department of Mathematics University of Science and Technology of China Institute of Mathematics and Mechanics of UB RAS Ekaterinburg 620219Russia

Abstract Let H be a subgroup of a finite group G. H is nearly SS-embedded in G if there exists an S-quasinormal subgroup K of G, such that HK is S-quasinormal in G and H∩ K≤HseG, where HseG is the subgroup of H, generated by all those subgroups of H which are S-quasinormally embedded in G. In this paper, the authors investigate the influence of nearly SS-embedded subgroups on the structure of finite groups.

关键词： S-quasinormal subgroup Nearly SS-embedded subgroup Sylow sub-group p-nilpotent group Supersolvable group

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