نظرية الرسومات GRAPH THEORY )الرسومات املتماثلة )
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1 151 ريض نظرية الرسومات ( الرسومات المتماثلة( مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) جامعة الملك سعود كلية العلوم قسم الرياضيات تمارين 151 ريض نظرية الرسومات GRAPH THEORY )4-2( )الرسومات املتماثلة ) Isomorphic Graphs إعداد : مالك عبدالرحمن زين العابدين ه
2 151 ريض نظرية الرسومات ( الرسومات المتماثلة( مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) الرسومات المتماثلة Isomorphic Graphs
3 د) 151 ريض نظرية الرسومات ( الرسومات المتماثلة( مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) ) عدد الدورات التي طول كل منها في G يساوي عدد الدورات التي طول كل منها في. H )ه( عدد مركبات الرسم G يساوي عدد مركبات الرسم. H
4 151 ريض نظرية الرسومات ( الرسومات المتماثلة( مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات )
5 151 ريض نظرية الرسومات ( الرسومات المتماثلة( مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) تمارين س 1 : في التمارين من )1( إلى )33( بي ن ما إذا كان الرسمان المعطيان متماثلين أم ال و علل إجابتك. Q.Show that the graphs G = (V,E) and H = (W, F), displayed in the Figure, are isomorphic. )1( )2(
6 )3( 151 ريض نظرية الرسومات ( الرسومات المتماثلة( مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) )4( )5( )6(
7 )7( 151 ريض نظرية الرسومات ( الرسومات المتماثلة( مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) )8( )9( )11(
8 مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) نظرية الرسومات ( الرسومات المتماثلة( 151 ريض )11( )12( )13( )14(
9 مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) نظرية الرسومات ( الرسومات المتماثلة( 151 ريض )15( )16( )17( )18(
10 مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) نظرية الرسومات ( الرسومات المتماثلة( 151 ريض )19( )21( )21( )22(
11 مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) نظرية الرسومات ( الرسومات المتماثلة( 151 ريض )23( )24( )25( )26(
12 مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) نظرية الرسومات ( الرسومات المتماثلة( 151 ريض )27( )28( )29(
13 مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) نظرية الرسومات ( الرسومات المتماثلة( 151 ريض )31( )31( )32( )33(
14 151 ريض نظرية الرسومات ( الرسومات المتماثلة( مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) س 2 : عين جميع الرسومات الثنائية التجزئة التامة غير المتماثلة و التي عدد رؤوس كل منها 7 Q. List all nonisomorphic complete bipartite graphs with 7 total vertices? n س 3 : إذا كان G رسما بسيطا عدد رؤوسه فأثبت أن س 4 : عين جميع الرسومات البسيطة ذاتية التتميم التي عدد رؤوس كل منها. 5 Q.Set all simple self complementary graphs with 5 vertices س 5 : عين جميع الرسومات البسيطة غير المتماثلة التي عدد رؤوس كل منها 5 و عد أضالع كل منها. 3 Q.. List all nonisomorphic simple graphs with 5 vertices and 3 edges?
15 س 6 : 151 ريض نظرية الرسومات ( الرسومات المتماثلة( مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) إذا كان G رسما بسيطا عدد رؤوسه n و عدد أضالعه 55 و كان عدد أضالع هو 08 فاحسب. n Q.Let G Be a simple graph with n vertices and 56 edges. If have 80 edges, find the value of n? س 7 : جد مع التعليل عدد أضالع الرسم المتمم للرسم. Q. Find the number of edges for the complementary graph of. Explain the answer? س 8 : عين جميع الرسومات البسيطة غير المتماثلة التي عدد رؤوس كل منها 4 و عد أضالع كل منها. 3 Q. List all nonisomorphic simple graphs with 4 vertices and 3 edges?
16 س 9 : 151 ريض نظرية الرسومات ( الرسومات المتماثلة( مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) هل يوجد رسم G له 7 أضالع و يحقق G وض ح إجابتك. Q.Is there exist a graph G with 7 edges satisfies G? explain the answer. س 11 : إذا كان G رسما بسيطا درجات رؤوسه 3,3,3,3,3,4 فأوجد عدد أضالع ( الرسم المتمم ). Q.Let G be a graph with the degree sequence 3,3,3,3,3,4.Find the number of edges of?. إذا كان G س 11 : رسما بسيطا عدد رؤوسه n و عدد أضالعه 5 فجد ضعف عدد أضالع الرسم المتمم Q. Let G be a graph with n vertices and 5 edges, find the double edges of? إذا كان G س 12 : رسما بسيطا عدد رؤوسه n يساوي. 43 و عدد أضالعه. 35 جد n إذا علمت أن عدد أضالع الرسم المتمم Q. Let G be a graph with n vertices an 36 edges. Find value of n if have 42 edges?
17 151 ريض نظرية الرسومات ( الرسومات المتماثلة( مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) س 13 : منتظم أيضا و عدد رؤوسه. n أثبت أن الرسم المتمم إذا كان G رسما بسيطا منتظما من النوع r و احسب عدد أضالعه Q. Let G be a simple regular graph of r degree and n vertices. Show that is a regular, and find the number of edges?. G إذا كان G رسما عدد رؤوسه 5 و عدد أضالعه. 7 هل ذاتي التتميم علل إجابتك س 14 : Q. Let G be a graph with 6 vertices and 7 edges. Decide whethere G is self complementary? Explain the answer? Q. Find the number of edges of the complementary of? س 15 : جد عدد أضالع الرسم المتمم للرسم
18 151 ريض نظرية الرسومات ( الرسومات المتماثلة( مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) س 16 : إذا كانت المصفوفة التالية هي مصفوفة التجاور للرسم G فبي ن فيما إذا كان G ذاتي التتميم. س 17 : أوجد عدد أضالع الرسم المتمم للرسم Q. Find the number of edges of ( the complementary graph of ). س 18 : أوجد عدد أضالع الرسم المتمم للرسم ثم بين فيما إذا كان الرسم ذاتي التتميم. Q. Find the number of edges of the complementary graph of? Decide whether is self complementary?
19 أ) ب) مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) نظرية الرسومات ( الرسومات المتماثلة( 151 ريض س 19 : س 21 : س 21 : ليكن L الرسم الممثل بمصفوفة الوقوع المبينة : أوجد عدد أضالع الرسم المتمم للرسم L بين فيما إذا كان الرسم L ذاتي التتميم. و لماذا ) )
20 151 ريض نظرية الرسومات ( الرسومات المتماثلة( مالك عبدالرحمن زين العابدين ( جامعة الملك سعود قسم الرياضيات ) س 22 : ليكن G رسما بسيطا ممثال بمصفوفة التجاور المقابلة : ارسم ( الرسم المتمم للرسم ) G بين فيما إذا كان الرسم G ذاتي التمميم أم ال )i( )ii(
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