21 Ax) -2 -3 Use the graph to find each of the following:

Q: 6. Draw the complete bipartite graph K4,5 and it's complement. Find the number of vertices |V| and…

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Q: 1. Is there a connected graph whose degree are: a. 5, 3, 2, 2, 2, 1, 1

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: QUESTION 14 Total number of edges of a complete graph which has 9 vertices is None 36 edges 12 edges…

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Q: prdinates of point k on the graph could only k

A: We can find and identify the coordinates of K as below

Q: 4- 3 C

A: By the theorem of Eulerian graph, a graph is Eulerian graph if and only if degree of each vertex is…

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

A: Given:  To determine: The complete graph so that it has the type of symmetry indicated.

Q: 2. Show that there is no simple graph with six vertices of which the degrees of five vertices are 5,…

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Q: 3. а) Define the following terms as used in graph theory: i) regular graph ii) simple circuit

A: A graph is called a regular graph as graph it degree of each vertex. is equal. A graph is called k…

Q: The number of even degree vertices in a simple graph must be even. O true O false

A: To state true or false given statement.

Q: Give an example of a graph with five vertices of degree 1, and six vertices of degree 2. If you…

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Q: 1.Show that K3,3 is non planner graph

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Q: grapii wi tnat пave degree o and the remaining two have degree 4? If yes, then draw the graph and if…

A: As per our guidelines only (a) has been solved. We know that, "If G is any undirected graph, then G…

Q: 33. Which of the following statements is/ are true? I. Adding an edge to a path graph will always…

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Q: If a simple graph Gis having 12 vertices and 9 edges then its complement graph G will have O 12…

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Q: Prove that any planar graph must have a vertex of degree 5 or less.

A: Let GV,E is a planar graph. To prove: G must have a vertex of degree 5 or less I am showing this…

Q: Let G be a simple graph with exactly 11 vertices. Prove that G or its complement G must be…

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Q: Quèstion 16 If a Graph has 10 vertices each of degree 5, then the number of edges in the graph…

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Q: If v is a leaf of a graph and u is the vertex adjacent to v, then ε(v) = ε(u) +1. State whether…

A: Solution:- Given:- v is a leaf of a graph and u is the vertex adjacent to v. Yes, this statement is…

Q: 15 Total number of edges of a complete graph which has 9 vertices is 36 edges None 12 edges 18 edges…

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Q: Consider the graph given above. Give an Euler trail through the graph by listing the vertices in the…

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Q: Prove that any graph with at least two vertices must have two vertices of the same degree.

A: Let G be a graph with n vertices where n≥2 To prove: G must have two vertices of same degree  On the…

Q: Does there exist a simple connected graph with vertices of the following degrees? If so, draw the…

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Q: You have a simple graph G with three vertices and three edges. How many subgraphs can be made from…

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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: (a) Is there an undirected graph with 7 vertices such that five of the vertices have degree 3 and…

A: As per guidelines only (a) is to be solved. Here, we use properties of undirected graph.

Q: Which one of the following is a quadratic graph? 10 10 10 10 -10- -10 -10 O bksb 2021

A: We have to check

Q: 19 Can a graph with three vertices of degrees 2, 1, 4 exist? Yes No

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Q: 8. 1 Use Kuratowski's theorem to prove that the following graph is not planar.

A: To Prove- Use Kuratowski's Theorem to prove that the following graph is not planar.   Theorem used-…

Q: Let A be the graph b How many walks of length 13 are there between node a and node f? Your answer…

A: Consider the provided graph,

Q: Which of the following graphs are bipartite? I

A: A graph is bipartite iff graph does not contains any odd cycle.

Q: 2.29. Is this graph planar (the edges cross each other in the middle but there is no vertex there)?

A: Planar graph: When a connected graph can be drawn without any edges crossing it is called planar.…

Q: If a graph has 5 vertices then 'By the Handshaking Theorem', each vertex can have degree 9. True…

A: Given: Statement: If a graph has 5 vertices then by handshaking theorem, each vertex can have degree…

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…

Q: 9. A planar graph has faces (including the external face) composed of eight 3-cycles and eighteen 4-…

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Q: 4. Is the following graph strongly connected? If not, is it weakly connected? 1

A: Digraph: strongly and weakly connected

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

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Q: for which values of m and n are km,n regular?

A: Given: A simple graph is called regular if every vertex of this graph has the same degree. A regular…

Q: (b) A planar graph has 10 edges and its dual graph has j edges, for some integer j. What is this j?…

A: Use the properties of planar graph and their dual graphs. Use the relation between the number of…

Q: Are the ff. two graphs isomorphic? 一 一 一 1. 1. 1. 1. -

A: To find Are the ff. Two graphs isomorphic.

Q: (a) An undirected simple graph has 1000 vertices of degree 6 and 200 vertices of de- gree 2. This…

A: Since you have posted a multiple question according to guildlines I will solve first  question for…

Q: QUESTION 11 Total number of edges of a complete graph which has 9 vertices is None 18 edges 12 edges…

A: The total number of edges in complete graph of n vertices are (n(n-1))/2

Q: True or False: There exists a simple graph with 9 vertices each of degree 5. O True O False

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

A: Given: The given figure is

Q: Consider the following. (a) Give the number of edges in the graph. edges (b) Give the number of…

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Q: Which statement is TRUE? a. The sum of all degrees of a cycle graph equals 2* number of edges  b.…

A: To determine: Which statement is TRUE. a. The sum of all degrees of a cycle graph equals 2* number…

Q: b) Determine whether there is an Euler trail from vzto V6 in the following graph. If there is, find…

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Q: ve the problem. raph has 5 vertices: four vertices of degree 3 and a vertex of degree 2. How many…

A: Here we have to find the number of edges in given graph.

Q: Suppose G is a simple undirected graph with n vertices. If G is self-complementary, prove that…

A: ↦A Simple undirected graph G is meant by a graph which have no multiple loop. there exist at most…

Q: Is it possible to have a connected graph with six (6) vertices of degrees 1, 1, 2, 2, 2, and 3? If…

A: in a connected graph, the sum of degree of all the vertices is twice the number of edges. therefore…