4. How many edges does a graph have if its degree sequence is 5, 2, 2, 2, 2, 1? Draw such a graph. (Hint: Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees of its graph vertices.)

Q: A city is built on the banks of a river and some islands in the river. The map below shows the…

A: Remark: An Euler path is a path that uses every edge of a graph exactly once. The graph is given as

Q: onsider a graph on 4 vertices in the shape of a square. What is the degree sequence of the graph?…

A: According to the given information first it is required to find the degree sequence of the graph of…

Q: If a graph has 5 edges, how many vertices does it have?

A:

Q: How many connected components does this graph have? What is the total degree of the graph?

A: From the given graph. We say a connected component is when the number of edge is removed then the…

Q: Determine all possible degree sequences fo

A: Isolated vertex:         " A vertex is said to be an isolated vertex if a vertex of degree zero  (no…

Q: How many edges does this graph have?

A:

Q: A city is built on the banks of a river and some islands in the river. The map below shows the…

A: Given: A map of a city built on the banks of a river and some islands in the river. The map below…

Q: 4. Construct all degree sequences for graphs with four vertices and no isolated vertex.

A: Construct all possible degree sequences with four vertices and no isolated vertex

Q: Construct a simple graph that is a tree with vertices P, Q, R, S, T, U such that the degree of T is…

A:

Q: Show that every graph with n vertices and k edges, n> k has n – k components.

A:

Q: An undirected graph is called complete if every vertex shares and edge with every other vertex. Draw…

A: Complete Graph:Every vertex shares an edge with every other vertex.Denoted by Kn, where n is the…

Q: 15. (a) Suppose a graph has 5 vertices and 7 edges, and every vertex has degree 2 or 3. How many…

A: The handshaking theorem states that the sum of the degrees of all vertices in a graph is twice the…

Q: number

A:

Q: 1. The degree sequence of a graph is a list of the degrees of the vertices of a grap in decreasing…

A:

Q: Explain why there are no simple graphs with these degree sequences. (а) 6,6,5,3,2,2,2 (b)…

A: a) Given degree sequence is        6,6,5,3,2,2,2 We prove there is no simple graph with this degree…

Q: Construct a connected bipartite graph that is not a tree with vertices O, P, Q, R, S, T. What is the…

A:

Q: Give an example of a bipartite graph on 10 vertices that is (a) 2-regular; (b) 3-regular; (c)…

A: (a) 2-regular (b) 3-regular

Q: 3. Which graph is the rooted tree that is formed from the tree in figure K, when: • vertex u is…

A:

Q: represent

A:

Q: The graph G₁ has 6 vertices, all of degree 3. How many edges does G₁ have? The graph G₂ has 8…

A:

Q: A graph G has 8 vertices and 11 edges. What is the total degree (sum of degrees) of this graph?

A:

Q: Draw a graph that models the connecting relationships in the floorplan below. The vertices represent…

A: The graph that models the floor plan is:

Q: How many possible ways can you draw a graph using 5 vertices? Show all steps of your calculation.

A: To find the number of possible ways to draw a graph using 5 vertices.

Q: a) Is it possible to construct a simple graph with degree sequence 2, 2, 2, 2, 2, 3, 3, 3 Either…

A: we know that in simple graph we have even number of vertices of odd degree. Now, we have given a…

Q: 5. Let G be a graph with degree sequence (5, 5, 5, 4, 4, 3, 3, 3, 1, 1, 1, 1). Does there exist a…

A:

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

A: Solution

Q: Determine whether the following statement is true or false. In the graph of a tree, the number of…

A: To determine true or false.

Q: Define the graph Sn,k as the graph with vertex set the set of k-elements subsets of {1, 2, . . . ,…

A: The main objective is to draw Sn,k graph for n=4, k=2 and n=4, k=3. we have to find the edges a

Q: 28. Chromatic questions (ExH). Find the chromatic number for each graph below. (a) (b) (c) (d)…

A: To find- Find the chromatic number for each graph below.

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

A:

Q: b 5. which of the following sequences of vertices determine Not a walk? O a, b. g.f,c b Of d. e,c, b…

A:

Q: Suppose G is a simple connected graph with degree sequence (4, 4, 3, 2, 2, 2, 2, 1). a. Draw this as…

A: a)  Planar graph as shown below

Q: Draw 2 different graphs with the following vertex sequence. (4,3,3,2,2,1,1). Label each vertex with…

A: Graph theory, graph the graph using Degree sequence by using HANDSHAKING theorem

Q: Let H be the graph below: (a) How many trees, with vertex set [7], have H as a subgraph? (b) How…

A: NOTE : As per Bartleby guidelines, incase of multiple subparts, only first three are answered.…

Q: Show that it is not possible to creak graph the" degree with g vertices such that every a of vertex…

A: Given that  The no of vertices = 9 degree of each vertices =3 To show such graph is not possible.