(9) Consider a graph with the following set of vertices (v1, v2, v3, v4) and set of edges {el,e2,e3,e4}. Which of the following is a valid representation of a possible walk in the graph? "Select all that applies) Ovl v3 v2 v4 c4 el e3 v2 c2 v4 e4 v1 v1 v2 e3 e4

Q: Suppose a graph G has 15 vertices and 38 edges. Which of the following statements is true? O 1. G…

A:

Q: 29. Let G be a graph with vertex set VG and edge set Ec. Let V C VG and EC EG. Is there always a…

A:

Q: Let x and y be two adjacent vertices in the complete bipartite graph Kn,n,     n ≥ 3. Find the…

A:

Q: Give an example to show that if P is a (u, v)-path in a 2-connected graph G, then G does  not…

A: To show that if P is a u,v-path in a 2-connected graph G, then G does not necessarily contain a…

Q: 1. Suppose G is a planar graph with four faces of lengths 3, 4, 5, 6. How many edges are there in G?

A: Answer :-  a). Suppose G is a planar graph with faces of length 3, 4, 5, 6. How many edges are there…

Q: Consider a complete graph with 6 vertices labeled A, B, F. (a) If you can start at any vertex, how…

A: Step-1 Consider a graph with 6 vertices, For complete graph with n vertices there exist   n-1!2…

Q: Give an upper bound on the number e of edges of G in terms of n and g if G is a connected plane…

A:

Q: Eulerize this graph in the most efficient way possible, considering the weights of the edges. 2 2 2…

A: A graph is Eulerian if all the vertices are of even degree.

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: 1- Show an example of a subgraph, spanning subgraph, induced subgraph of the complete graph in…

A: Solution: The given graph is The subgraph is : Spanning Subgraph: Induced Subgraph:

Q: Does the following graph have a Hamiltonian circuit? v5 This graph has the following Hamiltonian…

A: Graph theory: Hamilton circuit

Q: Show that if u and v are the only odd-degree vertices in G, then there is a uv path G.

A: We prove this by induction on the number of vertices in G.   Case 1:   If the graph consists of…

Q: (9) Consider a graph with the following set of vertices (v1, v2, v3, v4) and set of edges…

A: In our graph, we have vertices and edges, or both are defined, and to obtain a walk we need to…

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: If a simple graph G is having I1 vertices and 9 edges then its complement graph G will have O 11…

A: Given, number of edges in graph G, EG=9 Number of vertices in graph G, n=11 We know that,…

Q: Consider the fuzzy graph on vertices a,b,c where o(a)=0.5,0(b)=0.25,0(c)=1 and…

A: It is known that, the complement of a fuzzy graph. G:σ,μ is a fuzzy graph G:σ,μwhere σ=σ and…

Q: Prove that if u is a vertex of odd degree in a graph, then there exists a path from u to another…

A: We have to prove :       If u is a vertex of odd degree in a graph, then there exists a path from…

Q: Find the number of paths of length 2 from a to c in the directed graph give a b d a 3 b|1 2 2 1 c| 2…

A: Given that,  The matrix representing the directed graph is    abc  dabcd0230122121101002

Q: Let G be a simple connected plane graph with 6 vertices. (a) (b) (c) (d) What is the largest number…

A:

Q: 3. A labeled Ks graph with labeled edges appears below. Which edge permutation is induced by the…

A: Solution:

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: 8S lt G be the directout graph in Fiy(6-7), Fig(6-7) Vs @ Find two mple paths from Vi tovr. Is…

A:

Q: 1. Consider the following graph: eg U5 e3 e7 es Ove e2 v3 es (b) Find all edges that are incident…

A:

Q: Let G = (V, E) be a k-connected graph, let æ E V, and let B C V\{x} such that |B| > k. Show that…

A: Fan: Let v∈V(G) and let A∈V(G)\{v}. A v,A-fan of size k is a collection of k paths P1,P2,...,Pk so…

Q: Let P be a path graph with n2 4 vertices. What is the length of a longest path in the complement of…

A: In the given question, concept of graph theory is applied. Graph Theory A graph is a figure made up…

Q: Prove that if G is a simple graph with n > 3 vertices and (",') +2 edges, then G is Hamiltonian. b)

A: In the given question we have to prove that a simple graph with vertices more than or equal to three…

Q: 8) Consider the directed graph below 1 point Ps P1 P2 PA The number of 2-step connections for this…

A: The adjacency matrix is given by A = 0010100010010100000101000 Then  A2 = 0010100010010100000101000…

Q: List all the odd vertices of the graph. b) According to Euler’s Theorem, does the graph have an…

A: (a) The odd vertices are the vertices that have odd degrees, that is, having odd number of edges…

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

A: Digraph: strongly and weakly connected

Q: Let G be a graph with vertex set VG and edge set EG. Let V C VG and EC EG. Is there always a…

A: Consider the given information.

Q: Which of the following graphs has four vertices and exactly one bridge? O A. O B. OC.

A: I have given an answer in step 2.

Q: 3) What is the adjacency matrix Ac for the following graph G based on the order of the vertices a,…

A: Note: Since you have asked multiple independent questions, we are only allowed to answer one. Thank…

Q: Consider a bi-partite graph, B, with two vertex sets of m vertices and n vertices. How many entries…

A: A Bi-partite graph B with vertex set m vertices and n vertices

Q: True or False: There exists a simple graph with 9 vertices each of degree 5. O True O False

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: 1. Draw the following graph and answer the three questions below. V ={Red, Yellow, Green}, where…

A: Vertices, V={Red, Yellow, Green} Edges, E={(Red, Yellow), (Yellow, Green), (Green, Red), (Red,…

Q: Consider a graph G where the vertices are points (a, b) with integer coordinates, and {(ai, bi),…

A: Given: Let us consider graph G, in which the vertices are integer-coordinated points (a,b), and (ai,…

Q: Consider a complete graph with 6 vertices labeled A, B, ... F. (a) If you can start at any vertex,…

A: Consider the given information.   (a)   First calculate the number of Hamiltonian circuit in 6…

Q: Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and B. Show…

A: Consider two sets Aand B with N labelled vertices and bipartite graphs between Aand B. Show by…

Q: Give an example of a non-planar graph that is not homeomorphic to K5or K3,3.

A: We can solve this using definition of planar graph.

Q: Let G be a simple connected plane graph with 6 vertices. (a) (b) (c) (d) What is the largest number…

A: Note - Acc. to Bartleby guidelines, we are supposed to do only first 3 subparts . If you want more…

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.

Q: 7. Give an (i) a non-planar graph that is not homeomorphic to K5or K3,3 example of

A: To find: A graph which is non planar and not homomorphic to K5 or K3,3. If the edges of the graph…

Q: Are the following directed graphs strongly connected or not? Explain why in detail? 3 4 A

A: A directed graph is said to be strongly connected if there is a path between any pair of vertices in…

Q: 1. Let C(G,k) denote the decision problem of whether the undirected graph G = subset of vertices V'…

A: Let C(G,k) denotes the decision problem, Let G is the given graph and k be the subset of the graph…

Q: a. Let V = {x, y, z, u, v}. How many distinct graphs are there on the vertex set V with exactly 6…

A: We have given graph V{x,y,w,u,z} We need to calculate a)graph having 6 edges. b) The trail which is…

Q: Let G be a simple graph with nonadjacent vertices v and w, and let G+e denote the simple graph…

A: Given that, v and w are non-adjacent vertices in G. (1): G+e the simple graph formed by adding the…