Consider the following. (a) Give the number of edges in the graph. | edges (b) Give the number of vertices in the graph. vertices (c) Determine the number of vertices that are of odd degree. vertices (d) Determine whether the graph is connected O Yes O No (e) Determine whether the graph is a complete graph. O Yes O No

Q: 8. (a) Can you draw a graph with at least two vertices for which all the vertices have different…

A: consider the graph  A has valence 1 Vertex B has valence 2 Vertex C has Valence 3 Vertex D has…

Q: What is the chromatic number of the graph K33, the graph with 33 vertices each connected to each…

A: We have graph K33 with 33 vertices connected to each other. So, we have a complete graph K33

Q: 3. Either draw a graph with the specified properties or explain why no such graph exists. a. Graph…

A: Given problem is :

Q: (a) Show that in a simple graph with n > 2 vertices, at least two vertices have the same degree.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 3. In the following, draw a graph having the given properties or explain why no such graph exists.…

A: To find- In the following, draw a graph having the given properties or explain why no such graph…

Q: prove that any connected graph G in which every edge is contained in a cycle cannot be disconnected…

A: Want to prove:  If G is a connected graph in whichevery edge 'e' is contained in a cycle then g-{e}…

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: 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: 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: The following graph is k-edge connected. What is the value of k?

A:

Q: When n = 3, there are nonisomorphic simple graphs.

A:

Q: 1. Determine if the graph is a complete simple graph. If it is not a complete simple graph, explain…

A:

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

A:

Q: DRAW A PROPER GRAPH FOR THE SOLVED QUESTION.

A: The given system of equations is: 2x-y=1  ...(1)2x-y=2   ...2 Both the equations are linear with two…

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: n47- AdjacencyGraph [bigGraph, VertexLabels - "Name" ) Ou= G17. Is the graph above a connected…

A:

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

A:

Q: For many applications of matchings, it makes sense to use bipartite graphs. You might wonder,…

A: As per our guidelines we can solve only first three parts. If you want other subpart to be answered…

Q: 13. Determine whether the following graph is strongly connected. b.

A:

Q: Let G be a simple graph with n vertices, which is regular of degree d. By considering the number of…

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: draw the graph or explain why the graph cannot exist: (a) A simple graph on 5 vertices with 12…

A:

Q: Consider the following graph. V5 (V3 V4 V2 eg V6 V1 Compute the degree of each vertex. V1 V2 V3 4 V5…

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

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: 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: Out(4) G3. List the set of vertices for the graph above:

A:

Q: how that the following graphs are planar: 1.b. 1.c.

A: To prove the graphs are to be planar, draw the graphs on the plane such that their edges intersect…

Q: Discrete math. graph theory . Please answer (a)

A: K-regular graph means each vertex has k degree.

Q: Let G be a graph with 10 vertice and 5 components. If a vertex is removed from G, the number of…

A: Answer: 9 and 4

Q: Give an example of obtaining the complete graph?

A: A graph is a complete graph if  each pair of graph vertices is connected by an edge. The complete…

Q: The following graph is an example of a complete graph Kn. What is the integer value for n in…

A: A simple underected graph in which there exist an edge between every pair of vertices is called…

Q: Which statement is FALSE? a. A k-regular graph is also a complete graph  b. A bi-partite graph is…

A:

Q: 3. For the graphs below, determine (a) the number of edges in the graph, (b) the number of vertices…

A: Hello, thanks for your question but according to our policy I am answering the first three subparts…

Q: Consider an undirected, connected, simple graph with n vertices. What are the minimum and maximum…

A:

Q: 2. Determine if the following two graphs are isomorphic. а) b)

A: (a) let us suppose  graph 1 graph 2 we have to find if graph is isomorphic or not

Q: Consider the following graph. (Enter your answers as comma-separated lists.) A graph with 5 vertices…

A:

Q: Let G be a graph with n vertices and m edges, and let v be a vertex of G of degree k and e be an…

A: Degree of a vertex is defined as that from a vertex how many distinct edges are connected. Number…

Q: Are the following 2 graphs isomorphic? Discuss your answer with appropriate reasoning.

A: Given two graphs. From the first graph, d(u1)=3d(u2)=3d(u3)=2d(u4)=2d(u5)=3d(u6)=3

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

A:

Q: Show that there are exactly 2"(-1)/2 labelled simple graphs on n vertices. How many of these have…

A:

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

A:

Q: What is the minimum number of colors you need to color the vertices of this graph such that if two…

A:

Q: The of a vertex is the number of edges along the unique path between it and the root. o Degree Child…

A: The ..... of a vertex is the number of edges along unique path between it and the root

Q: Let G be a simple undirected graph with 16 edges. If all vertices have degree at most four, which of…

A: Let G be a simple graph with n vertices and e edges. Use the following formula, to determine the…

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

A: