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1. (2 pts) Prove that C[t] is not isomorphic to Clr.y]/(y2-13) as a C- algebra. (It follows that the affine line A1 is not isomorphic to the variety X CA2 defined by the equation y 1. (2 pts) Prove that C[t] is not isomorphic to Clr.y]/(y2-13) as a C- algebra. (It follows that the affine line A1 is not isomorphic to the variety X CA2 defined by the equation y
10. Two of the graphs in Figure 1.25 are isomorphic. FIGURE 1.25 (a) For the pair that is isomorphic, give an appropriate one-to-one corre- spondence (b) Prove that the remaining graph is not isomporhic to the other two
1. Draw all non-isomorphic simple graphs with 5 vertices and 0, 1, 2, or 3 edges; the graphs need not be connected. Do not label the vertices of your graphs. You should not include two graphs that are isomorphic. 2. Give the matrix representation of the graph H shown below.
(2) [20 ptsl Which of the following pairs of graphs are isomorphic? Explain why (2) [20 ptsl Which of the following pairs of graphs are isomorphic? Explain why
1. Show that S3 is not isomorphic to U(14) 2. How many automorphisms are there from Z2 to itself?Define each of them.
1. Draw all non-isomorphic simple graphs with 5 vertices and 0, 1, 2, or 3 edges; the graphs need not be connected. Do not label the vertices of your graphs. You should not include two graphs that are isomorphic. 2. Give the matrix representation of the graph H shown below. 3. Question 3 on next page. Place work in this box. Continue on back if needed. D E F А B
Determine whether the given pair of graphs is isomorphic, if the graphs are not isomorphic provide an argument? kes A-33 S:3 B B) 5 5 4
Determine whether the given pair of graphs is isomorphic, if the graphs are not isomorphic provide an argument? A) F G B) 4) Consider the following weighted graph G below
Just trying to figure out what the subgroup is isomorphic to? 2. Find the subgroup (fo, T]) of Sa, where σ (2134 What is the subgroup isomorphic to? 23 order (σ ): 2 L (12) (34) Su
3. For cach pair of graphs, determine whether or not they are isomorphic. If they are isomorphic, write down an isomorphism between them (a map between vertices that extends to a map between edges). If they are not isomorphic, give a graph invariant that distinguishes them. d 3 2 b (a) a 2 4 7 h (b)