b) Is the following graph isomorphic to Q4? If yes, give an isomorphism from Q4 to this graph. Otherwise, find a copy of Q3 in it. c) If v is a cut-vertex of a graph G, then v is also a cut-vertex of every induced subgraph of G containing v. Prove or disprove.

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Q: Let G be the (3,4)-complete bipartite graph. (a) List all non-isomorphic subgraphs with 5 vertices…

A: Part(a) Solution:Let be the (3,4) complete bipartite graph K3,4      These are the 11…

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Q: Suppose a graph G is regular of degree r, where r is odd. (a) prove that G has an even even number…

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Q: (d) Show that the pair of graphs are not isomorphic by showing that there is a property that is…

A: (d)  To prove that the pair of graphs are not isomorphic by showing that there is        a property…

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Q: Suppose that a graph G has n vertices, and all vertices have degree greater than or equal to“,.…

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Q: Draw all non-isomorphic graphs of order n with 1<n<4.

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A: According to the property of isomorphism , Should have the same number of edges. Have same number…

Q: .34. Consider the graph G in Fig. 8-58. Find: (a) degree of each vertex (and verify Theorem 8.1);

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Q: 13. Determine whether the following graph is strongly connected. b.

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Q: Let Gbe a simple graph with at least 11l vertices, and let G be its complement. (i) Prove that Gand…

A: Given: G is a simple graph with at least 11 vertices and Ḡ be its complement.

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Q: G is a graph on n 21 vertices such that both G and its complement have an Euler trail. (Recall that…

A: To do: Draw a simple graph G such that "G is a graph with n≥1 vertices such that both G and its…

Q: 7. Check if the following graphs G and H are isomorphic.

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Q: Give an example to show that if P is a (u, v)-path in a 2-connected graph G, then G does not…

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Q: Let G be a connected graph. Prove: (a) If G contains a cycle C which contains an edge e, then G – e…

A: Part (a):   A connected graph is a graph in which there is a path joining each pair of vertices, in…

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Q: Prove that every graph G on {1,... n} which is acyclic and has n 2 edges has exactly 2 connected…

A: Given: To prove the given statement as follows:

Q: Prove: For any graph r with six vertices ror r complementary contains C3

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Q: Let G be a simple graph. Show that the relation R on theset of vertices of G such that uRv if and…

A: Given: A simple graph is G. To prove: That the set of vertices of G is such that uRv if and only if…

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A: Let L be the set of undirected graphs. A undirected graph is bipartite if its nodes can be divided…

Q: subgraph of a nonplanar graph is nonplanar

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Q: 1. For the pair of graphs shown, • if the graphs are not isomorphic, explain why not; • if the…

A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below…

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A: Answer: 9 and 4

Q: Show that the petersen graph is nonplanar.( Hint :show that the graph is contradictible to k5.

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Q: 2. Determine if the following two graphs are isomorphic. а) b)

A: (a) let us suppose  graph 1 graph 2 we have to find if graph is isomorphic or not

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Q: 9. Verify that Euler's formula does not hold for a graph that is not connected: count the vertices,…

A: Euler's formula for v vertices, e edges and f faces is: v-e+f=2 For the given graph we have vertices…

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Q: Prove the following. 1. Prove that the number of odd vertices of a graph is even.

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Q: Let G be a 2-connected graph. Prove that if G has no even cycles, then G is isomorphic to an odd…

A: k-Connected graphs: A graph is said to be k-connected if it has more than k vertices and remains…

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Q: Prove that if  v0 and v1  are distinct vertices of a graph  G  = (V,E) and a path exists in G from…

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Q: 3. Find the degree of the vertices of the following graphs and verify the handshaking theorem.

A: Degree of a vertex is the number of edges incident on it.

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A: Suppose G is disconnected. We want to show that G¯ is connected. So suppose v and w are vertices. If…

Q: Which of the following graphs contain a subdivision of K3,3 as a subgraph

A: The solution is given below in detail in which we found no graph contains a subdivision of K3, 3 1)

Q: Let G=(V, E) be a graph such that • V| ≥ 3, G has exactly 2 leaves, and in G all the non-leaf…

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Q: Prove that if G is a graph of order p and has size greater than ¹) then G is connected. 2

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Q: (3) Determine whether or not each of the following graphs is planar. If planar, show a planar…

A: As per our company guidelines, we can solve one question at a time. If you want other question to be…

Q: Let G be a simple graph with nonadjacent vertices v and w, and let G+e denote the simple graph…

A: Given that, v and w are non-adjacent vertices in G. (1): G+e the simple graph formed by adding the…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.