(a) What is the degree of each vertex in the K7 graph shown below? (b) Does...
2. For the graph given below, a. Write out the degree of each vertex. b. Find an Eulerian Circuit. (Write out the sequence the vertices are traversed. E.g. A-B-C-A.) c. Find a Hamiltonian Path.
North Bank South Bank How many vertices are in your graph? How many edges are in your graph? Give the degree of each vertex: deg(A) = , deg(B) = , deg(C) = , deg(North) = deg(South) = Does this graph have an Euler Circuit, an Euler Path, or Neither?
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...
Recall the definition of the degree of a vertex in a graph. a)
Suppose a graph has 7 vertices, each of degree 2 or 3. Is the graph
necessarily connected ?
b) Now the graph has 7 vertices, each degree 3 or 4. Is it
necessarily connected?
My professor gave an example in class. He said triangle and a
square are graph which are not connected yet each vertex has degree
2.
(Paul Zeitz, The Art and Craft of Problem...
Write down true (T) or false (F) for each statement. Statements are shown below If a graph with n vertices is connected, then it must have at least n − 1 edges. If a graph with n vertices has at least n − 1 edges, then it must be connected. If a simple undirected graph with n vertices has at least n edges, then it must contain a cycle. If a graph with n vertices contain a cycle, then it...
5. The in-degree of a vertex in a directed graph is the number of edges directed into it. Here is an algorithm for labeling each vertex with its in-degree, given an adjacency-list representation of the graph. for each vertex i: i.indegree = 0 for each vertex i: for each neighbor j of i: j.indegree = j.indegree + 1 Label each line with a big-bound on the time spent at the line over the entire run on the graph. Assume that...
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?
For a directed graph the in-degree of a vertex is the number of edges it has coming in to it, and the out- degree is the number of edges it has coming out. (a) Let G[i,j] be the adjacency matrix representation of a directed graph, write pseudocode (in the same detail as the text book) to compute the in-degree and out-degree of every vertex in the Page 1 of 2 CSC 375 Homework 3 Spring 2020 directed graph. Store results...
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. 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...