3. In a planar drawing of a graph, each face is bounded by a circuit. Make a planar drawing of a graph that is equivalent to the graph shown, in which faces are G. bordered by the same circuits as the given graph but where the face bordered by A -B-C-G-F-A is in the infinite face. E

Q: Construct the intersection graph of the following collection of sets: 4 = {0,+2, 14, 16, ±,..} A, =…

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Q: 2. Show that the following graph is not planar. USM 1999 083 IVERS

A: Given- To show that the given graph is not planar.

Q: 40. The following chart represents the vertices and edges of a graph. A check mark indicates that…

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Q: 6. Dctermine whether cach of the given graphs has a Hamilton circuit. If it does, find such a…

A: To find- Determine whether each of the given graphs has a Hamilton circuit. If it does, find such a…

Q: 1. Suppose G is a planar graph with four faces of lengths 3, 4, 5, 6. How many edges are there in G?

A: Answer :-  a). Suppose G is a planar graph with faces of length 3, 4, 5, 6. How many edges are there…

Q: For a complete graph, match the number of Hamilton circuits for a given vertices. n = 3 n = 4 6 n =…

A: Hamilton Circuit : A circuit that must pass through each vertex of a graph once and only once. Being…

Q: How many different labelled graphs are there on the vertex set [n]? Justify your claim.

A: Given Vertex set n Let vertex V=1, 2, 3, ........., n Each graph G with a vertex V is determined by…

Q: Suppose that D, G, E, A, H, C, B, F, D is a Hamilton circuit in a graph. a) Find the number of…

A: a) Since there are 8 different vertices in the Hamilton circuit, number of vertices in the graph is…

Q: Let G be simple connected planar graph. If G has 8 vertices and 11 edges, in how many regions will…

A: Euler formula for planar graph: Let G be a connected planar graph, and let n, e and f denote,…

Q: Consider a bipartite graph on the set A = {1,2,3, 4, 5, 6} and B = {7,8,9, 10, 11, 12}, there is an…

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Q: How many circuits are there in the graph?

A: only two circuis are there.  Which are 2342 and 2432

Q: 6. Which of the next sets establish a bipartition of the graph in Fig.1? a) {a, h, g, b, f} and {i,…

A: To determine which of the given sets establish a bipartition of the graph. Here we will use the…

Q: How many different simple graphs are there om the vertex set [n]?

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Q: 10. Does the graph below have an Euler circuit? If so, find one. If not, explain why. A B FO E D

A: Given a graph : We have to check the graph below have an Euler circuit or not. We know, A circuit is…

Q: Question 58 There exists a simple graph H with 6 vertices and 7 edges such that H has an Euler…

A: In a simple graph, only one edge exists between any two vertices. Also, each edge starts and ends in…

Q: The number of edges in a graph with 12 vertices each of degree 6 is O 72 O 1 O 12 O 36

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Q: Suppose we are told that a connected graph cuts the plane into 211 regions. How many more edges than…

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Q: 1) How many possible ways are there to match or pair vertices between A and B?

A: For any queries please let me know through comments. I will try to reply ASAP! Please upvote if…

Q: 1.1 How many simple graphs are there of four vertices? Draw all of them.

A: As per our guidlines we are supposed to solve only one question that is the first problem. For the…

Q: How many vertices will the following graphs have if they contain: (a) 12 edges and all vertices of…

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Q: a. Let V = (x, y, z, u, v). How many di exactly 6 edges? (Note that for graphs G₁ = (V, E₁) and G₂ =…

A: (a) We are given that the set of vertices is V=x, y, z, u, v. We are asked to find the number of…

Q: A hamilton circuit exists in the ff. graph: O False O True

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Q: 4. Imagine that the diagram shown below is a map with countries labelled a-g. Is it possible to…

A: Given - Imagine that the diagram shown below is a map with countries labelled a-g.  To find - Is it…

Q: 3. Recall that Km,n denotes a complete bipartite graph on (m, n) vertices. a. Draw K4,2- b. Draw…

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Q: How many edges are in the Hasse diagram that represents the poset ( {1, 3, 4, 6, 8, 12, 16, 18), I…

A: Solution

Q: The number of edges in a graph with 10 vertices each of degree 7 is O 35 O 14 O 70

A: Given that  Number of vertices of the given graph=10 Degree of each vertices=7 To find Number of…

Q: QUESTION 3 The number of edges in a tree with 16 vertices is O At least 15 O At most 15 O Possible…

A: To find the number of edges in a tree with 16 vertices

Q: Which of the following sequences of degrees of vertices in a multigraph has a Euler circuit? A…

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Q: Consider the following statements: S: There exists a connected simple graph with 6 vertices and 5…

A: We have to verify the given statements.

Q: If there are 10 vertices in a tree, there must be edges. O 10 O 9 O 11 O 8

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Q: How many vertices will the following graphs have, if they contain: (a) 18 edges and all vertices of…

A: According to the rule I only do the first three

Q: is The number of edges in a complete bipartite graph K5 O 15 O 20 O 30 O 10

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Q: 1. Which of the next sets establish a bipartition of the graph in Fig.1? a) {a, h, g, b, f } and {i,…

A: Graph has an odd cycle which is a-e-c-a And if a graph contains odd cycle can not be bipartite.

Q: The number of edges in a graph with 8 vertices each of degree 7 is O 7 O 56 28 O 14

A: We have to solve given problem:

Q: Determine whether the following statement is true or false. O False In the graph below, the path B,…

A: Hamilton Path: A Hamilton Path is a path that goes through every Vertex of a graph exactly…

Q: A graph is connected if and only if one vertex is neighbor to all other vertices O True O False

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Q: 20 8. Compute the crossing number for each of the following graphs.

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Q: Which of the following sequences of degrees of vertices in a multigraph has a Euler circuit? A…

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Q: 4. Find the perimeter of rectangle MNOP with vertices M(-2, 5), N(-2, -4), O(3, –4), and P(3, 5). MN…

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Q: 40. Find the Euler circuit and Hamilton circuit for the given graph if there is one. E

A: An Euler circuit is a circuit in which every edge of the graph is transversed only once such that…

Q: 2. Show that the graphs formed by deleting one edge from Ks and K33 are planar.

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Q: Answer T if the graph or tree exists as described and F if it does not. 1. Connected graph with 9…

A: # we are entitled to solve one question at a time, please resubmit the other questions if you wish…

Q: 11. Determine if the following graph is bipartite graph. If it is, show how to divide its vertices…

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Q: The following graph has a Hamilton circuit: 2 13 7 9. 11 10 14 13 12 15 17 16 O True False 00

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Q: 1. Which of the following is NOT a circuit in the graph? A B E Figure 1 А) СВЕС B) ABEA C) BCDCB D)…

A: (1) First we have to know about a circuit in a graph. Circuit: A circuit is a path which ends at the…

Q: A graph is defined as a pair (V, E) where V is a finite set of elements called vertices, and E is O…

A: Given that a graph is defined as a pair V,E where V is a finite set of elements called vertices.

Q: The number of edges in a graph with 10 vertices each of degree 5 is O 10 O 25 O 50

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Q: Construct a connected simple graph, that has no circuit, with vertices M, N,0, P, Q, R, S, T, U such…

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Q: When a vertex Q is connected by an edge to a vertex K, what is the term for the relationship between…

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Q: How many vertices will the following graphs have, if they contain: (a) 18 edges and all vertices of…

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