(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
For Exercises 15-20, decide if the two graphs are isomorphic. If so, give the function or functions that establish the isomorphism; if not, explain why. 15 Ca as d6 al 7 ?? ci a2 e7
17. (G2) Draw two non-isomorphic graphs with 4 vertices. Carefully explain how you know they are not isomorphic
17. (G2) Draw two non-isomorphic graphs with 4 vertices. Carefully explain how you know they are not isomorphic
which of these graphs are isomorphic?
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2. a) Determine whether the following graphs are isomorphic or not. If so write an isomorphism, if not explain why. 1 b 2 a 6 3 f d 5 4 e Graph A Graph B. b) Is the graph A bipartite. If not, find a vertex v such that A - v bipartite? c) Does the graph A have an Eulerian circuit? If not find an edge e such that A - e has an Eulerian circuit.
Homework Problems Problem 12.8. Determine which among the four graphs pictured in Figure 12.24 are isomorphic. For each pair of isomorphic graphs, describe an isomorphism between them. For each pair of graphs that are not isomorphic, give a property that is preserved under isomorphism such that one graph has the property, but the other does not. For at least one of the properties you choose, prove that it is indeed preserved under isomorphism (you only need prove one of them)...
Find the smallest positive integer n such that there are non-isomorphic simple graphs on n vertices that have the same chromatic polynomial. Explain carefully why the n you give as your answer is indeed the smallest.
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.
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
For each integer k > = 2, give an example of k non-isomorphic regular graphs, all of the same order and same size.
Are the following graphs planar? If so, show a planar representation and if not, explain why not. ь.
Are the following graphs planar? If so, show a planar representation and if not, explain why not. ь.