2. Give an example of a graph with at least four vertices, or prove that none exists, such that: (a) There are no vertices of odd degree. (b) There are no vertices of even degree. (c) There is exactly one vertex of odd degree. (d) There is exactly one vertex of even degree. (e) There are exactly two vertices of odd degree.

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

A:

Q: 1. Consider the given graph. (a) Determine the number of vertices of the graph. (b) Determine…

A:

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

A:

Q: the number of edges in the graph   (b.) give the number of vertices in the graph (c.) determine the…

A: a)  There are 10 edges in the graph. Hence, the number of edges in the graph is 10. b) The vertices…

Q: Show that in a simple graph with at least Two vertices there must be two vertices that have the same…

A:

Q: Use the Handshaking Lemma to show that a graph G always has an even number of vertices with odd…

A:

Q: Among each pair of the CEOs of N companies there is (a) mutual like; (b) mutual dislike; (c) neutral…

A:

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

A:

Q: At a cupcake stall at the Greenwich market, the owner is selling six different types of cupcakes.…

A:

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

A:

Q: The degree of every vertex of a graph G is one of three consecutive integers. If, for each of the…

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

A: Solution

Q: 3. (a) Is it possible to have a 4-regular graph with 15 vertices? If no, explain why. If yes,…

A: To find-  Is it possible to have a 4-regular graph with 15 vertices? If no, explain why. If yes,…

Q: Prove that the sum of the degrees of the vertices of any finite graph is even.

A:

Q: State and prove closed Graph theorem.

A:

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

A: Sol

Q: 3. Prove the following statement: If G is a graph with at least 2 vertices, then a(G) > 2 or w(G) 2…

A: Induction Proof A graph with 2 vertices has either 0 or 1 edges, and in either case, the two nodes…

Q: In a high school class, there are students of different talents (ex. music, art, debate, sports,…

A: 1. Consider the information provided in the problem, The vertices of the graph is the total number…

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: (10). Find the in-degree and out-degree of each vertex of the following directed graph G. V4 V2

A: Given that the directed graph G:                  . To find the in-degree and out-degree of each…