Consider the following two graphs: G1 V1 = {a,b,c,d,e, f, g} E1 = {{a,b}, {a,d},{b,c}, {b,d}, {b, e}, {b, f}, {c,g}, {d,e}, {e, f},{f,g}}. G2 V2 = {v1, v2, V3, V4, V5, V6, V7}, E2 = {{v1, V4}, {v1, v5}, {V1, 07}, {v2, V3}, {v2, 06}, {v3, v5}, {V3, v7},{V4, V5}, {U5, V6}, {v5, 07}} (a) Let f : G1 → G2 be a function that takes the vertices of Graph 1 to vertices of Graph 2. The function is given by the following table: b d f a e te | (x)f Does f define an isomorphism between Graph 1 and Graph 2? V5 V1 V6 V2 V3 V7 (b) Define a new function g (with g + f) that defines an isomor- phism between Graph 1 and Graph 2. (c) Is the graph pictured below isomorphic to Graph 1 and Graph 2? Explain.

Q: Determine whether the two graphs are equivalent.

A: Two graphs are equivalent if they have the same sets of the vertices and the same set of edges. In…

Q: Mark the critical points on the following graph. ate,0.4 2+ 1.6 12 0.8 0.4 -3 -2 3 -04 0.8 -12 -1.6…

A: The critical points are the point where function has maximum and minimum. For that need to find…

Q: Based on K1, K2, and K3, which graphs are not simple graphs? b a b. к, у K2 Y K3 Y K, and K2 a b K2…

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Q: now that the graphs are not planar: 2.b. 2.c.

A: A graph is called planar if no edge of the graph crosses the the other edge except on vertices of…

Q: Draw pictures of the specified graphs. Graph H has vertex set {y1, y2, y3, y4, y5} and edge set {e1,…

A: As specified in the question, there are 5 vertices and 4 edges in a graph H.Edge e1 connects y1 to…

Q: Work out the adjacency list for the following graph. 1 2 3 5

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Q: Let G = (V, E) be the undirected graph described below and let E' = {(A, F), (F, D), (F, H), (A,…

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Q: A в B D D E F Graph 1 Graph 2

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Q: Which of the following graphs are connected? VI i a. (a) (b) (a) h VA (b) V3 (c) w X

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Q: Consider the following graphs, each with vertex set V = {1, 2, 3, 4, 5, 6}, G = (V, E1), where E…

A: Given that,  V = { 1,2,3,4,5,6 }G1 = ( V, E1 ), where E1 ={{1,2},{2,3},{2,6},{3,5},{4,5},{5,6}}G2=…

Q: Find the strongly connected components of this graph? * b O {a, b, c, d, e, f, g, h}. None of them.…

A: Answer : {a, b, c, d, e, h}, {f}, and {g}. Hence, option (vi) is correct.

Q: a b a lc a bde Ce e

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Q: Which of the following graphs represents y = -x²? -10 -2 0 -2 6 10 විය. 24 6 09 2 8 10

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Q: 2. Draw a picture of the graph G specified as follows: Vertex set = {V1, V2, V3, V4, V5} Edge set =…

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Q: 1. For the following graphs, find the strongly connected components. a. a b d b. b a d f e

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Q: Q. Show that the following two graphs are isomorphic 2. 3 10 1. 9 •5 L. a •b e d

A: Two graphs G1 and G2 are isomorphic if there exists a match- ing between their vertices so that two…

Q: Let G be a graph with vertex set V and edge set E. If |V] = 7, what is the largest value that |E||…

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Q: In Problem ,draw a complete graph so that it has the type of symmetry indicated.

A: Given,

Q: Consider the following graphs, each with vertex set V = {1, 2, 3, 4, 5, 6}, G1 = (V, E), where E =…

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Q: Describe the end behavior of the graph shown. 10 6. 8. 7. 5. 4 3. -6 3 4. 6. 7. 8. 9 10 -10 -9 -8 -7…

A: The end behavior of a function f describes the behavior of the graph of the function at  the…

Q: V1={a,b,c,d} E1={{a,b},{a,c},{a,d},{c,d}} V2={a,b,c,d} E2={{a,b},{a,c},{b,c},{c,d}} are these…

A: We know that two graphs are equal if they have set vertex set as well as same edge set.

Q: Consider the following graph. V(G) = {v1, v2, v3, v4},  e(G) = {e1, e2, e3, e4, e5, e6}, E(G) =…

A: we first draw the given graph. the paths from V1 to V4 are as follows1.e1,e5 2.e4  3.e6,e3…

Q: Show that for any planar graph, v-e+f=2. v=vertices e=edges f=faces

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Q: Which of the following graphs is NOT planar? II. III.

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Q: Indicate if each of the two graphs are equal. a b a a bde d e e |c d (a) Figure 1: Left: An…

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Q: Answer True or False. The pair of graphs is not isomorphic. VI vS V6 V3 VA O True O False

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Q: Show that the two drawings represent the same graph by labeling the vertices and edges of the…

A: Consider the two given graph.Let imagine that the edges of the given graph are strings and the…

Q: Which of the following four graphs on five vertices is not isomorphic to any of the other three?…

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Q: show that the two drawings represent the same graph by labeling the vertices and edges of the…

A: Consider the two given graph.In the right graph, it is observed that one edge is connected to the…

Q: Determine whether these two graphs are isomorphic. Explain why or why not. a b h d G

A: We see, in H, swxyzvuts is a 8-cycle. But, in G, maximum length cycle is 6-cycle. that is girth of G…

Q: Suppose the graphs of f(x) = x2 and  g(x) =  2 x  are drawnon a coordinate grid where the unit of…

A: Given:          Graphs:                          f(x)=2xg(x)=2x   Let's draw the sketch of the…

Q: C) Explain why there cannot exist a simple graph of order 11, where the vertices have degrees 1, 1,…

A: Given: A simple graph of order 11 where the vertices have degrees 1,1,2,2,2,2,3,4,4,6,6.

Q: a. Prove that the sum of the degrees is equal to twice the number of edges. b. Check whether it is a…

A: From the graph Degrees of a = 5  b = 6 c = 3 d = 6 As a ,b and d have loop which contribute to two…

Q: Which of the following is/are  non-Eulerian graph? a. Graphs B C D ONLY b. Graphs B C D E c.…

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Q: Select the graph that represents the point 3, D. O A. B. AY

A: topic - polar coordinate system

Q: Find the connected components of each graph. (i) G = (V, E). V = {a, b, c, d, e}.  E = ∅   (ii) G…

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Q: A D Graph 1 Graph 2

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Q: а. B 1 2 3. E D F G 6 b. 3 5

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Q: Consider the following graph; b Which of the following graphs are subgraphs of the graph above? OA.…

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Q: 2. 10 1. 9 .5 6 a •b h e•

A: Let G(V1 , E1) be a graph with vertex set V1=1,2,3,4,5,6,7,8,9,10 and H(V2 , E2) be a graph with…

Q: List all reduced subgraphs with 4 vertices for the following graph. e2 €3 e6 €4 e5 d e7

A: A graph H is called a sub-graph of G if, VH⊂VG EH⊂EG IH is the restriction of IG to EH

Q: Choose the graph of y = Inz 1. 4. 1. 1. 1.

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Q: Which of the following graphs are bipartite? G G H E H E I K OA В I K H Y OC

A: Bipartite Graph :        A graph G is called Bipartile if theverctices can be divided into two…

Q: Give an example of a non-planar graph that is not homeomorphic to K5or K3,3.

A: We can solve this using definition of planar graph.

Q: Q5. Determine whether the following graphs G and G' are isomorphic. If so, give the vertices and…

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Q: Find the number of edges for each of the following graphs. a. Kn b. Km,n

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Q: Determine whether the two graphs are equivalent. A в с D E F equivalent O not equivalent B D LL F A…

A: Solution:

Q: Make each graph with its correct equation. 3. -78 -5 -4 -3-2 -1 4. 123456 tut 3-2-1 12345 -2 5. 6.…

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