ooooo TMobile '5' 7:35 PM 4 0' >3 32% E]. E platform.virdocs.com C5 7' \\ WU I In 1 and 2, graphs are represented by drawings. Dene each In 5- graph formally by specifying its vertex set, its edge set, and a by 13 table giving the edge-endpoint function. corre . 5. l 61 o \"I \"2 \"4 '32 v3 e3 2. In 3 and 4, draw pictures of the specied graphs. 3. Graph G has vertex set {vb v2, v3. v4, v5} and edge set {91, e2. e3. e4}, with edge-endpoint function as follows: 7- n e n 4. Graph H has vertex set {1:1, 11;, v3, v4, 0,} and edge set {ch 82, e3. e4} with edge-endpoint function as follows: ooooo T-Mobile '5' 7:36 PM 4 0 >3 32% E]- 4. Graph H ins verb): set {01.01, 113, 0', us} and eds: set {ch :3, 23, ed with edge-endpoint function as follows: *For exercises with bin 11me or letters, solutions are given in Appem solution is given. The symbol 1k gnals that an exercise is more challengin nmlnmm.mmmuth unwamuhwbnhuhmnubnluw \"simulate-diluting! \"WomannlmyauuhmnumupunwL-nigt ooooo TMobile '5' 7:39 PM 4 0' >3 31% . platform.virdocs.com C I\" D II <657> '0 2. In the graph below, determine whether the following walks are trails, paths, closed walks, circuits, simple circuits, or justwalks. & \"192929303949495028291811'0 b. vzvavwsvz c- vwzvsvwsvm d. vzvtvsvzvsvwz e. vov5u2v304v2vl f. 1151;40sz and consider the walk vlelvzezvl. a. Can this walk be written unambiguously m vlvzvl? Why? b. Can this walk be written unambiguously as 8181? Why? _ < > m [D E ooooo TMobile '5' 7:37 PM 4 0' >3 32% -' platform.virdocs.com C \\ m I 'I' In each of 1725, either draw a graph with the specied proper- ties or explain why no such graph exists. l7. Graph with ve vertices ofdegrees l, 2, 3, 3, and 5. 18. Graph with four vertices of degrees 1, 2, 3, and 3. l9. Graph with four vertices of degrees 1, l, l, and 4. 20. Graph with forn- vertices of degrees 1, 2, 3, and 4. 21. Simple graph with four vertices of degrees 1, 2, 3, and 4. 22. Simple graph with ve vertices of degrees 2, 3, 3, 3, and 5. 23. Simple graph with ve vertices of degrees 1, l, l, 2, and 3. 24. Simple graph with six edges and all vertices of degree 3. 25. Simple graph with nine edges and all vertices of degree 3. 26. Find all subgraphs of each of the following graphs. 3. \"2 b. Cu \"2 31 v1 '2 \"I I'0 \"I \"3 27. a. In a group of 15 people, is it possible for each person to have exactly 3 'iends? Explain. (Assume that friendship is a symmetric relationship: Ifx is a friend of y, then y is a frind of x.) b. In a group of 4 people, is it possible for each person to have exactly 3 friends? Why? 28. In a group of 25 people, is it possible for each to shake hands with exactly 3 other people? Explain. 29. Is there a simple graph, each of whose vertices has even degree? Explain. < > [1] ooooo TMobile '5' 7:39 PM 4 0' >3 31% . platform.virdocs.com C <657> '0 I\" D II a. Howmanypathsaretherefromatoc? b. How many trails are there from a to c? c. How manywalks aretherefrcma too? 6. An edge whose removal disconnects the graph of which it is a part is called a bridge. Find all bridges for each of the following graphs. 3 v 1 u; b. \"0 v1 v2 \"3 U3 U5 U4 \"8 U6 Us cl 7. Given any positive integer n, (a) nd a connected graph with n edges such that removal of just one edge discon- nects the graph; (b) nd a connected graph with n edges that cannot be disconnected by the removal of any single _ < > m [D E ooooo TMobile '5' 7:40 PM 4 0' >B 31% E platform.virdocs.com C Qi <659> . \"s 22. The following is a oor plan of a house. Is it possible to enter the house in room A, travel through every interior doorway of the house exactly once. and exit out of room E? Ifso, how can this be done? Find Hamiltonian circuits for each of the graphs in 23 and 24. 23. 24