.Given the following degree of the vertices of an undirected graph H = {4,1,5,3,4,3}, we can conclude that: A. Graph H is a graph and there is an end vertex in graph H B. Graph H is a graph and there is an isolated vertex in graph H C. Graph H is not a graph D. We cannot conclude anything.

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…

A:

Q: 7. Is this the graph G planar? If so, then determine the faces and the edges.

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Q: Is it possible for a graph with 35 vertices and 100 edges to be planar? O Yes O No

A:

Q: 3. Show that the two drawings represent the same graph by labeling the vertices and edges of the…

A: Give figure is

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

A:

Q: Can the following graphs drawn in plane without edge crossings? a

A: Given: Graphs, To determine: Whether the given graphs can be drawn without crossing.

Q: b a K2 Y к, у K, and K2 K3 and K, K2 and Kg d All of them

A: We use definition of Complete graph.

Q: Determine the sum of the in-degrees and out-degrees of each graph shown in Figure 1. Show the…

A:

Q: The number of edges for a complete graph K6 is O 20 O 30 O 15 O 10

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Q: 2. Give an example of a graph with at least four vertices, or prove that none exists, such that: (a)…

A: The objective is to give an example of a graph with at leas four vertices, or prove that none…

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

A:

Q: B A D C

A:

Q: Which of the following statements about a connected graph is always TRUE?         A path of…

A: Solution: From the definition of the connected graph there should be path between any two pair of…

Q: B2. a. Draw four graphs such that each graph contains a cycle of length 3, 4, 5, and 6 respectively.…

A: We have to draw four graphs so that each graph contains a cycle of length 3, 4, 5 and 6…

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

A:

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: We say that two distinct edges in a graph are adjacent if there is a vertex incident to both (the…

A: Solution

Q: 1. Find all 6 subgraphs of the following graph. 22 O

A:

Q: 42. Which of the following graphs contains a cut-vertex? A. Complete graph K3 B. cycle C4 C. path P2…

A: Sol

Q: 0 . Identify whether or not the following graph is strongly connected or weakly connected. the graph…

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Q: Show that every simple graph on n vertices subgraph of K.

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Q: OD

A: Remark: A path in a graph is a sequence of vertices with the property that each vertex in the…

Q: Sketch the complete graph with number of vertex 6.

A: Complete graph: A simple and undirected graph is said to be a complete graph if every pair of…

Q: 2. Let G be a connected (simple) planar graph where the number of vertices = 8. What can be said…

A: In a simple connected planer graph with n vertices can have at most 3n−6 edges.

Q: 31. In any undirected graph the sum of degrees of all the nodes A. must be even B. are twice the…

A: Sol

Q: Suppose there are ten Middlebury College students in a room. One of those ten is friends with all of…

A: We are given the following information, There are 10 students in a room. One of them have…

Q: What is the number of connected components for each of the following graphs? (a) b a d

A: A connected component of an undirected graph is a maximal set of nodes such that each pair of nodes…

Q: The graph with edges AC and BD is a connected graph. True False

A: We have to find , the graph with edges AC and BD is a connected graph or not.