(a) G is a connected graph with 6 vertices and 5 articulation points.

Q: The graph G is a planar connected graph. It has 23 edges, and 8 faces. How many vertices does G…

A: I have given the answer in the next step. Hope you understand that

Q: Is hypercube graph Q4 planar? If not can you provide any bounds on it crossing number?

A: No, hypercube graph Q4 is not a planner graph.

Q: 10. A policeman wants to patrol a neighbarhood, but anly wants to walk down the street once. Based…

A: This is a problem of Graph Theory.

Q: (a) Give the number of edges in the graph.

A: answer is in next step. please give a like !!

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: ne graph of

A: The given straight line intersects the x-axis at the point (1, 0) and the y-axis at the point (0,…

Q: Let G be a graph such that every vertex has degree 4 and the number of edges is 12. How many…

A: Simply keep in mind that vertex degree multiplied by number of vertices is two times number of…

Q: 10. Give an example for each of the following situations, or explain why they cannot happen: (a) A…

A: a) A simple graph on four vertices with total degree 2.b) A simple graph whose vertices all have…

Q: What is the smallest number of colors you need to properly color the vertices of K3.3 ? That is,…

A:

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

A: Given that, This is the graph is an upper horizontal half parabola whose vertex at -4, 0 crosse…

Q: d. Add up all the indegrees, and add up all the outdegrees. What do you notice? Can you explain why…

A:

Q: 12. Let G be a graph in which there is no pair of adjacent edges. What can you say about the degree…

A: See picture

Q: Let G be a complete graph with n vertices. a. How many edges does G have? Explain why. b. What is…

A:

Q: The graph G is a planar connected graph. It has 25 edges, and 9 faces. How many vertices does G…

A:

Q: (b) Give an example of a disconnected simple graph on n vertices in which every vertex has degree…

A: We need to give an example of a disconnected simple graph on n vertices in which every vertex has…

Q: 4. Edge FE is adjacent to which edges? 5. Does this graph have any bridges?

A: 2) 4. Recall: In a graph, two edges are said to be adjacent, if there is a common vertex between the…

Q: Can a graph with nine vertices and nine edges exist? Explain wy no such graph exists or draw the…

A: To verify whether a graph with 9 vertices  & 9 edges exist or not.

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

A:

Q: what is K-connected of a graph ? And give an example

A: Definition: A graph is said to be K- connected graph or K edge connected graph if after removed less…

Q: 4. Recall that a cut-vertex of a graph G is a vertex of G whose removal makes the graph dis-…

A: Definition: A vertex whose deletion along with incident edges results in a graph with more…

Q: If G1 is a simple graph with 20 edges and G has 25 edges, how many vertices does G1 have?

A:

Q: If a graph has 8 vertices, then what is its order? Answer:

A: We have given a graph which has 8 vertices. We know that  Order of a graph is cardinality of…

Q: 1. Let G be a complete graph with n vertices. a. How many edges does G have? Explain why. b. What is…

A: Solution of given problem as follow:

Q: If a graph G has n vertices, all of which but one have odd degree, how many vertices of odd degree…

A:

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

A:

Q: A graph with 7 vertices and 10 edges is shown. Vertex a is connected to vertex b, to vertex d, and…

A: According to the given information, First it is required to draw the graph from the given…

Q: 11. If G is a simple graph with 4 vertices, then the maximum possible value for the sum of the…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: what is the edge - connectivity in a graph ? And give an example

A: Edge - Connectivity in a graph : Let ‘G’ be a given connected graph.Then the minimum number of edges…

Q: 4a Let n > 4. What is the maximum possible number of edges in a graph with n vertices and n-2…

A:

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 G is a graph, then the sum of its vertex degrees is nonnegative and even.

A:

Q: What do the in-degree and the out-degree of a vertex in adirected graph modeling a round-robin…

A: To Define : In-degree and Out-degree of a vertex in a directed graph modeling a round-robin…

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: State whether the following statement is true or false. Justify your answer with a short proof or a…

A: Consider the general case, Let G be k-edge connected graph then we shall rove that G is k connected.…

Q: Draw a graph with two loops around vertex e, with end vertices a and f, with multiple edges on…

A:

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: B: Fined the dual graph for Jollowing graphs the

A: Given

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

A: Digraph: strongly and weakly connected

Q: G is a graph on 6 vertices with exactly

A: (b) G is a graph on 6 vertices with exactly two biconnected components:

Q: Let G be a graph with exactly 10 vertices and 27 edges. Suppose that each vertex has degree 3, 5, or…

A:

Q: 1. (a) What is the maximum number of edges that a bipartite planar graph with 10 vertices can have?…

A:

Q: G9. Draw a graph with 4 vertices each of degree 2.

A:

Q: 12. If G is a simple graph with vertices a, b, c, d, e and d(a) = d(b) = d(c) = 3 (d = degree), then…

A: Here we apply Hand-shaking lemma for simple graph.

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.

Q: Question 4. Let K, be the complete graph on n vertices. How many edges does it have? Justify your…

A: Given that, the complete graph kn has n vertices. Number of the edges of this complete graph=nn-12

Q: Draw a graph with four vertices in which two vertices are of degree 2 and two vertices are of degree…

A: We have to solve given problem:

Q: The complementary graph G' of a simple graph G hasthe same vertices as G. Two vertices are adjacent…

A:

Q: in a graph What is K-edge connected And give an example

A: A graph, is said to be k-edge connected if even after removing k-1 edges the graph is still…