14 In the following graphs, do you think graph a and b have the same meaning? If not, what are their differences (10 points)
Q: Given the following adjacency matrix: A В D E G H 1 B 1 1 1 1 1 D 1 1 1 1 F 1 G 1 H. Create a graph…
A: Here have to determine Adjacency Graph.
Q: For the following graph, find the vertices adjacent to vertex 2: 1 2 3 A) 1 в) оз c) 0 1 3 (D) о 12…
A: A graph is a set of vertices and edges and it is represented as G = (V, E) where G is a graph, V is…
Q: 7. The two problems below can be solved using graph coloring. For each problem, represent the…
A: a. Let the vertices denote the teams and the edges as the game played between them. This problem can…
Q: a. Prove by Kuratowski's theorem that the two graphs below are not planar E F 2 7 8 b. Show that a…
A: A Kuratowski's theorem state that a finite graph G is planar if it is not possible to subdivide the…
Q: Draw a graph with four vertices of degrees 1, 2, 2, and 7 or else explain why no such graph exists.
A: It states that the sum of degrees of the vertices of a graph is equal to twice the number of edges.…
Q: B2. a For the following graph: B E F 1- Determine whether the graph is bipartite or not. 2- Write…
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Q: ii. 1 4. Represent the above undirected graph using i. adjacency matrix adjacency list 3 2 4 5
A: Solution: a> The nearness matrix, generally conjointly known as the affiliation matrix, of a…
Q: Plot the following in a line graph
A: The question is to plot the data in a line graph. As no software is mentioned here Excel has been…
Q: Are the two graphs in the figure isomorphic? If there are isomorphic, label the vertices o show the…
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Q: Take 8 different capital letters and place them into the vertices of a graph. Show:…
A: “Since you have posted a question with multiple sub-parts, we will solve first two subparts for you.…
Q: 10.Find the number of vertices, the number of edges and the degree of each vertex in a given…
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Q: 2. Use the Bellman-Ford algorithm to calculate the shortest paths from node A to every other node in…
A: Given : Given Graph with negative and positive weights. The task is to find the shortest path…
Q: Graph Coloring, continued (b) Find the chromatic number of the cubical graph (shown below). Be sure…
A: Chromatic Number: Chromatic Number is the minimum number of colors required to color any graph such…
Q: 4 1 2 3 5 4. Represent the above undirected graph using i. adjacency matrix ii. adjacency list
A: First lets understand adjacency matrix and adjacency list representation: i)Adjacency matrix: is an…
Q: 3. Draw all subgraphs of this graph a
A: A Subgraph of a graph can be defined as a graph that includes the set of vertices from the given…
Q: b) Does each of these lists of vertices form a path in the following graph in Figure 2? Which paths…
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Q: From the graph G given below identify the number of vertices and edges A B C Vertices 3 and Edges 4…
A: In a diagram of a graph, a vertex is usually represented by a circle with a label, and an edge is…
Q: {01] Assumen > 3. For which values of n do these graphs have an Euler circuit?
A: A connected multigraph (or graph) has an Euler circuit iff each of its vertices has even degree.(a)…
Q: Evaluate the Degrees and Neighborhoods of the vertices in the graphs G:
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Q: Give two different ear-decompositions of the following graph. Start both decompositions from the…
A: Answer: I have given answered in the handwritten format in brief explanation.
Q: 7. Check whether the given graph is Bipartite or not. Explain. 2 7 4 Also construct a proper…
A: 7. A graph can be considered as bipartite if it can be colored using any two colors in such a way…
Q: 3. Draw a connected graph with 4 vertices, each of degree 3.
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Q: A) [5] Given the order and size of a graph Gie 10 and 14 respectively. The degrees of vertices in G…
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Q: 5. Consider the following graph G (a) How many paths of length 5 are there between vertices 1 and 2?…
A: Hey there, I am writing the required solution based on the above given question. Please do find the…
Q: To determine If a graph contains a circuit that starts and ends at a vertex v, does the graph…
A: Simple Circuit: A circuit with no repeated vertices except the first and the last vertex. Consider a…
Q: Now draw a directed graph according to the above information.
A: Data about routes: FlightNumber Origin Destination 701 2 3 702 3 2 705 5 3 708 3 4 711…
Q: please generate and assign a random biconnected graph with n node and e edges in c++
A: The code is implemented in c++ language. The implementation is below implemented:
Q: Does there exist a simple graph with five vertices of the following degree? If so, draw such a…
A: The answer is given below.
Q: Question 5: Consider the following graph. Find the shortest path from 'a' to all other vertices…
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Q: Refer to the undirected graph provided below: B G What is the maximum length of a path in the graph?…
A: In the given undirected graph , we have answered the following questions.
Q: Q3) B- draw the following equations with label the axes, title for the graph and give legend for the…
A: Answer: I have done code and also I have attached code as well as code screenshot.
Q: 11. least one simple circuit of length 6, but G does not have any simple circuit of length 6. a) A…
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Q: 2 Letbe a graph with: (a) What is the largest number of edges that such a graph can have?…
A: Explanation: First of all, in graph there should be one edge from a typical vertex to another…
Q: 2 4 Given the graph above, list the following: A. All vertices: B. All edges (only from left to…
A: Given: Answer questions related to graph.
Q: For the undirected graph shown below, give the number of vertices, the number of edges, and the…
A: A graph consists of vertices and edges. Graph is a data structure that is non-linear in it's nature.…
Q: Prove that the degree of each face of G is three. Show all of your work and clearly explain, using…
A: given, vertices 12, edges=30. According to the Euler's formula:- V-E+F=2 Where F= number of…
Q: 4) Perform a BFS on the graph in Fig.1 starting at vertex A. When there is more than on option,…
A: Step 1 − Visit with starting vertex and the adjacent unvisited vertex. Mark it as visited. Display…
Q: V4 Draw the complement of the graph:
A: To draw the complement of the graph we will do a graph such that a number of vertices of the…
Q: Ex: what are the degrees and what are the neighbourhoods of the vertices in the graphs G and H ? a
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Q: Graph Complement and Planarity, (a) Let G be a 4-regular plane graph with 10 faces. Determine how…
A: Answer is given below .
Q: 39. Find the complement of each of the following graphs. a. b. V1. VI VA V2 V4 V2 V3 V3
A: Complement Graph: A graph with a same set of vertices as the original graph but the edges are the…
Q: Determine if the following graphs are isomorphic. If not, explain why not.
A: Isomorphic: In the isomorphic graph, a graph is a tweaked version of another graph. Two graphs (G1…
Q: Show the formal notation V(...) and E(...) of the graph that is described by the following adjacency…
A: The answer is
Q: 1. Draw the following graphs: (а) Кз, (b) Q4, (с) Кз,3, (d) W7. 2. What is the chromatic number of…
A: Given: Discreate math graphs.
Q: What is the chromatic number of the above graph? List the vertices in groups with the same color,…
A: Here in this question we have given a graph and we have asked to find out the chromatic number for…
Q: (a) A planar graph has 5 vertices and 3 faces. How many edges does it have?
A: The answer is
Q: Given the graph above, list the following: A. All vertices: B. All edges (only from left to right):…
A: The vertices are the nodes of graph which are represented using circles So, the vertices in given…
Q: 11. With the above information provided, draw a graph for the data provided. Indicate the weights…
A: The first question will be solved. Please upload another question again. 11) 1) Weighted directed…
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- This assignment requires the extension of your graph code to apply it to movement through a “world”. The world will be a weighted, directed graph, with nodes for the start position and target(s), and other nodes containing blocks, diversions, boosts and portals. For example, in a cat world, a dog may block you, toys may take your attention, food may give you more energy and portals may prove that cats are pan-dimensional beings. This structure could also be used to implement Snakes and Ladders, or other games. Your task is to build a representation of the world and explore the possible routes through the world and rank them. Sample input files will be available – with various scenarios in a cat world. Your program should be called gameofcatz.py/java, and have three starting options: * No command line arguments : provides usage information * "-i" : interactive testing environment * "-s" : simulation mode (usage: gameofcatz –s infile savefile) When the program starts in interactive mode,…The clique problem is finding cliques in a diagram. A clique is a set of vertices that are adjacent to each other. The 4-clique is a set of four knots all connected. So, in this example of the 4-clique problem, we have a graph with 7 vertices. A brute force algorithm searched all possible combinations of four vertices and found a set that formed a clique. If you want to understand more about it, the problem (and if possible read on). Note that the clique problem is NP-complete, so deterministic search is not practical for large graph sizes. This makes it an ideal candidate for evolutionary exploration. In this problem, we have to assume that we are given the problem of implementing the 4-clique problem as an evolutionary algorithm for an arbitrary graph with an arbitrary number of vertices (an n-vertex graph). If 4 cliques are found, the algorithm succeeds. 1. Provide an algebraic expression, in terms of n, for the size of the phenotypic search space (the number of possible…5. (This question goes slightly beyond what was covered in the lectures, but you can solve it by combining algorithms that we have described.) A directed graph is said to be strongly connected if every vertex is reachable from every other vertex; i.e., for every pair of vertices u, v, there is a directed path from u to v and a directed path from v to u. A strong component of a graph is then a maximal subgraph that is strongly connected. That is all vertices in a strong component can reach each other, and any other vertex in the directed graph either cannot reach the strong component or cannot be reached from the component. (Note that we are considering directed graphs, so for a pair of vertices u and v there could be a path from u to v, but no path path from v back to u; in that case, u and v are not in the same strong component, even though they are connected by a path in one direction.) Given a vertex v in a directed graph D, design an algorithm for com- puting the strong connected…
- Graph ColoringNote that χ(G) denotes the chromatic number of graph G, Kndenotes a complete graph on n vertices, and Km,n denotes the complete bipartite graph inwhich the sets that bipartition the vertices have cardinalities m and n, respectively. (c) Compute χ(K3,3). Justify your answer with complete details and complete sentences. (d) For n, m ∈ N, compute χ(Km,n). Do not justify your work. (e) Give an example of a graph G whose chromatic number is 3, but that contains no K3 as a subgraphAssume you are to write a program to analyze the social connection between students in MTSU. Each student is a node in a undirected graph. An edge is added between two nodes if these two students have close social connections, i.e., in the same club, or in the same department. Which would be a better representation for this graph? Question 45 options: adjacency matrix representation adjacency list representationA weighted, directed graph is a suitable representation to represent the daily airline routes flown by a small airline. The airline have the following daily flights: - Three flights from Cape Town to Johannesburg, - Two flights from Johannesburg to Cape Town. - Four flights from Johannesburg to Durban. - Three flights from Durban to Johannesburg. - One flight from Johannesburg to George. - One flight from George to Johannesburg.Draw the graph and answer the questions that follow. The graph that represents this problem is connected. A. True B. False
- Given a vertex set W = {1, 2, 3, 4}, solve for the following questions: (i) Knowing that edges are the same if and only if they have the same endpoint, how many different edges are possible? (ii) Suppose for this question that graphs are different if they have different sets of edges (they do not depend on if the graphs are isomorphic or not). How many simple graphs are there with the vertex set W? (iii) Draw the eleven nonisomorphic simple graphs that have four vertices.function [ ] = square_spectrum( L,N )%Activity 1 for CEN415 Summer 2022 x=linspace(0,2*L,200);f1=(-1).^floor(x/L);plot(x,f1)f2=0;for n=1:2:N, f2=f2+4*sin(n*pi.*x/L)/n/pi;endhold onplot(x,f2)hold offend 1-Run the function with L=3 and N=1 and upload the plotted graph use matlapCompute Lack of Cohesion in Methods (LCOM4) for the following class. Illustrate your calculation with an appropriate graph and partitions. What do you infer from the LCOM4 value of this class? [Do not include the member variables in your graph. The graph should include only member functions.] class LCOM4 { private int x, y, z, w; public void A() { for (int x= y; x<z; x++) w = w* x; } public boolean B() { return (x<0); } public boolean C() { return (y>0); } public void D() { if (C() || F()) A(); } public int E() { return (int) x/2; } public boolean F() { return (y<z); } public int G() { if (!B()) return E(); } }
- Let G be an undirected graph whose vertices are the integers 1 through 8, and let the adjacent vertices of each vertex be given by the table below: look at the picture sent Assume that, in a traversal of G, the adjacent vertices of a given vertex are returned in the same order as they are listed in the table above. Which statement of the following is correct? group of answer choices a) The sequence of vertices visited using a DFS traversal starting at vertex 1: 1, 2, 3, 4, 6, 5, 7, 8. b) The sequence of vertices visited using a BFS traversal starting at vertex 1: 1, 2, 3, 4, 6, 5, 7, 8. c) Both sequences are wrong. d) Both sequences are correct.3.Consider this graph data:- Jessica's buddy list: Meghan, Alan, Martin.- Meghan's buddy list: Alan, Lori.- Toni's buddy list: Lori, Meghan.- Martin's buddy list: Lori, Meghan.- Alan's buddy list: Martin, Jessica.- Lori's buddy list: Meghan.a. Compute the in/out degree of each vertex. Is the graph connected?b. Who is the most popular? Least? Who is the most antisocial?c. If we're having a party and want to distribute the message the most quickly, who should we tell first?A weighted, directed graph is a suitable representation to represent the daily airline routes flown by a small airline. The airline have the following daily flights: - Three flights from Cape Town to Johannesburg, - Two flights from Johannesburg to Cape Town. - Four flights from Johannesburg to Durban. - Three flights from Durban to Johannesburg. - One flight from Johannesburg to George. - One flight from George to Johannesburg. Draw a graph that represents this problem