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North Bank South Bank How many vertices are in your graph? How many edges are in...
Consider this map of the New Zealand North Island showing each of the regions in a different colour. (a) (4 marks) Draw a planar graph representing this map such that each region corresponds to a vertex and two vertices are connected by an edge if the two regions touch each other on the map (b) (2 marks) How many vertices in your graph have an even degree and how many vertices have an uneven degree? (c) (4 marks) What is...
(a) What is the degree of each vertex in the K7 graph shown below? (b) Does the graph possess and Euler Circuit, and Euler Path, or neither? (c) Find the number of edges in the graph.
A bipartite graph is a graph in which the vertices can be divided into two disjoint nonempty sets A and B such that no two vertices in A are adjacent and no two vertices in B are adjacent. The complete bipartite graph Km,n is a bipartite graph in which |A| = m and |B| = n, and every vertex in A is adjacent to every vertex in B. (a) Sketch K3,2. (b) How many edges does Km,n have? (c) For...
Draw a graph that models the connecting relationships in the floorplan below. The vertices represent the rooms and the edges represent doorways connecting rooms. Vertex F represents the outdoors. Determine whether the graph contains an Euler path or an Euler circuit. If either an Euler path or an Euler circuit exists, find one. B D The graph contains at least one Euler path, but no Euler circuit. An Euler path is DEFBFACFE. The graph contains at least one Euler circuit...
Draw a planar graph(with no loops or multiple edges) for each of the following properties, if possible. If not possible, explain briefly why not. b) 8 vertices, all of degree 3 ( how many edges and regions must there be) c) has exactly 7 vertices, has an euler cycle and 3 is minimum vertex coloring number Also please draw the graph.
Discrete Mathematics 6: A: Draw a graph with 5 vertices and the requisite number of edges to show that if four of the vertices have degree 2, it would be impossible for the 5 vertex to have degree 1. Repetition of edges is not permitted. (There may not be two different bridges connecting the same pair of vertices.) B: Draw a graph with 4 vertices and determine the largest number of edges the graph can have, assuming repetition of edges...
question 1 and 2 please, thank you. 1. In the following graph, suppose that the vertices A, B, C, D, E, and F represent towns, and the edges between those vertices represent roads. And suppose that you want to start traveling from town A, pass through each town exactly once, and then end at town F. List all the different paths that you could take Hin: For instance, one of the paths is A, B, C, E, D, F. (These...
a. b. c. d. e. What are the vertices? Is this graph connected? What is the degree of vertex C? Edge FE is adjacent to which edges? Does this graph have any bridges? Answer the following questions based on the graph below. 1w a. b. c. d. What are the vertices? What is the degree of vertex u? What is the degree of vertex s? What is one circuit in the graph?
a. Modify the graph by removing the least number of edges so that the resulting graph has an Euler circuit b. Find an Euler circuit for the modified graph starting at Awhose third and seventh vertices are G whose fit vertex is H. and whose fourth vertex is B. D a. Which edge() should be removed so that the resulting graph has an Euler circuit? Select all that apply A DH BAC D. FC BE GH OG BE H.BG DJ...
A graph has 21 edges, two vertices of degree 5, four vertices of degree 3, and all remaining vertices have degree 2. How many vertices does the graph have? 12 10 16 O 14