A Hamiltonian Cycle is any loop within a graph. A True False Question 25 2.38 Points...
Question 7 2.38 Points Solve the equation 2x+64=146. Calculate your answer to the nearest whole number. Do not put the x= in your answer. Only put the number value for your answer. Add your answer Question 8 2.38 Points Four teams will receive prize money based on their ticket sales. The total prize amount to be apportioned is $336. Determine the standard divisor based on the ticket sales. The ticket sales are: Applejacks: 54 tickets sold Broncos: 70 tickets sold...
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...
Let G=(V, E) be a connected graph with a weight w(e) associated with each edge e. Suppose G has n vertices and m edges. Let E’ be a given subset of the edges of E such that the edges of E’ do not form a cycle. (E’ is given as part of input.) Design an O(mlogn) time algorithm for finding a minimum spanning tree of G induced by E’. Prove that your algorithm indeed runs in O(mlogn) time. A minimum...
Question 3 2.38 Points If a graph has 36 points and 32 edges, then how many edges will be used to make it a tree? Add your answer Question 4 2.38 Points Calculate the next term in the arithmetic sequence that increases by 26, if the current term is 82. Add your answer
solve with steps 1. (20 points) True or false. Justify. Every planar graph is 4-colorable /2 The number of edges in a simple graph G is bounded by n(n 1) where n is the number of vertices. The number of edges of a simple connected graph G is at least n-1 where n is the number of vertices. Two graphs are isomorphic if they have the same number of vertices and 1) the same mumber of edges 1. (20 points)...
G3: I can determine whether a graph has an Euler trail (or circuit), or a Hamiltonian path (or cycle), and I can clearly explain my reasoning. Answer each question in the space provided below. 1. Draw a simple graph with 7 vertices and 11 edges that has an Euler circuit. Demonstrate the Euler circuit by listing in order the vertices on it. 2. For what pairs (m, n) does the complete bipartite graph, Km,n contain a Hamiltonian cycle? Justify your...
Question 4 10 pts Look at the weighted graph and choose the TRUE answers below (do not choose any FALSE answers) 1 B 4 4 2 5 D E 4 F 7 The graph has a minimal spanning tree of weight more than 15 The graph has a minimal spanning tree of weight less than 18 The graph has a Hamiltonian circuit ☺ ☺ ☺ ☺ The graph has an Euler circuit This graph is bipartite.
Let G = (V, E) be a weighted undirected connected graph that contains a cycle. Let k ∈ E be the edge with maximum weight among all edges in the cycle. Prove that G has a minimum spanning tree NOT including k.
5. (10 points) Solve TSP (Travelling Salesman Problem) for the following graph using 2-MST (Minimum Spanning Tree) algorithm. 18 12 15 15 13 10 15 Answer: a) the MST consists of edges its length is b) the Eulerian cycle is c) the Hamiltonian cycle is its length is
Question 1# (a) Let G be a connected graph and C a non-trivial circuit in G. Prove directly that if an edge e fa, b is removed from C then the subgraph S C G that remains is still connected. "Directly' means using only the definitions of the concepts involved, in this case connected' and 'circuit'. Hint: If z and y are vertices of G connected by path that includes e, is there an alternative path connecting x to y...