پديد آورنده :
هدايت، سارا
عنوان :
گراف هاي سيمپلكتيك به پيمانه ي pq و pn
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي محض ﴿جبر﴾
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع. به فارسي و انگليسي
استاد راهنما :
بيژن طائري
استاد مشاور :
قهرمان طاهريان
توصيفگر ها :
حلقه ي رده هاي مانده اي به پيمانه ي m , گروه سيمپلكتيك , گراف سيمپلكتيك به پيمانه ي m , تراياي كماني زير مدار
تاريخ نمايه سازي :
94/2/16
استاد داور :
عاطفه قرباني، محمدرضا ودادي
تاريخ ورود اطلاعات :
1396/09/26
چكيده انگليسي :
Symplectic graphs modulo pq and pn SARA HEDAYAT s hedayat@math iut ac ir December 15 2014 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Bijan Taeri b taeri@cc iut ac irAdvisor Dr Seyed Ghahraman Taherian taherian@cc iut ac ir2000 MSC 05C25 05B25 20F65Keywords Residue class ring modulo m Symplectic group Symplectic graph modulo m Arc transitive SuborbitAbstract This M Sc thesis is based on the following papers Fenggao Li Kaishun Wang Jun Guo Symplectic graphs modulo pq Discrete Mathematics 313 2013 650 655 Fenggao Li Kaishun Wang Jun Guo More on symplectic graphs modulo pn Linear Algebra and its Appli cations 438 2013 2651 2660 2 Suppose Zm denotes the residue class ring modulo m and U Zm denotes its unit group Let Zm be the set of all2 tuples a1 a2 a2 of elements in Zm such that a1 Zm a2 Zm Zm Define an equivalence 2 relation on Zm by a1 a2 b1 b2 U Zm a1 a2 b1 b2 2 Write a1 a2 for the equivalence class containing a1 a2 and let Zm be the set of all equivalence classes Let I 0 K 2 I 0where I is the identity matrix of order The symplectic group modulo m of degree 2 with respect to K 2 denoted by Sp2 m consists of all 2 2 matrices T over Zm satisfying T K 2 T t K 2 The symplectic 2 2 graph modulo m denoted by Spm is the graph whose vertex set is Zm and two vertices a1 a2 and b1 b2 are adjacent if a1 a2 K 2 b1 b2 t U Zm 2 modulo m in two cases m pq and m pn where p and qIn this thesis we study the symplectic graph Spm 2 are distinct primes and n is a positive integer We show that Spm is arc transitive in particular the the action of 2 symplectic group Sp 2 m on Spm which defined by Sp 2 Sp2 m Sp 2 m m x1 x2 x2 T x1 x2 x2 T 2 is transitive Also we determine the suborbits of symplectic group Sp2 m on Spm
استاد راهنما :
بيژن طائري
استاد مشاور :
قهرمان طاهريان
استاد داور :
عاطفه قرباني، محمدرضا ودادي
