(a) Consider the following graph. a d 90 g b h (i) Explain giving reason for your answer, why an Euler circuit exists. Indicate the Euler circuit. (ii) Determine a Hamilton circuit for the graph. (b) Draw the complete bipartite graph, K3,5.
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- full explanation...(a) Draw an undirected graph G1 represented by the following adjacency matrix: 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 Does G1 contain a Hamiltonian cycle? Explain (b) Determine which pairs of graphs G1 in part (a) and G2 and G3 shown below are isomorphic and which are not, and explain your answer. If you use any invariant property in your argument, explain why this property is an invariant. Tex our answer. t 2 G2 G3 5. 7 8.3. Determine whether the given graph has a Hamilton circuit. If it does, find such a circuit. If it does not, give an argument to show why no such circuit exists. M.. X
- 16.2. Find an Eulerian circuit of the graph of Figure 16.21 by the method of Theorem 16.2, starting with the circuit A-B-F-G-A. F E Figure 16.21. A graph with an Eulerian circuit.The line graph L(G) of a simple graph G is the graph whose vertices are in one-one correspondence with the edges of G, two vertices of L(G) being adjacent if and only if the corresponding edges of G are adjacent. Show that K3 and K, , have the same line graph. (i) (ii) Show that the line graph of the tetrahedron graph is the octahedron graph.5. (a) State Euler's formula for a planar graph G (explain any notation you use). (b) Explain why K, is not planar (explain in full any result you use from lectures).
- Consider the function as given. (a) Use a computer algebra system to graph the function and use the graph to approximate the critical numbers visually. (b) Use a computer algebra system to find f′ and approximate the critical numbers. Are the results the same as the visual approximation in part (a)? Explain.a 2 5 (a) 2 4 5 3 (b) Determine which of the graph have Euler circuit, Euler trail, Hamiltonian circuit. For each graph, if the graph does not have any of them, whether one or two of them explain why not. If it does have any of them, describe one for each of them. 3. 4)Please fast solve the problem Find and list the biconnected components of the graph in picture.
- 2. For the graph G below, determine k dDetermine whether the given graph has a Hamilton circuit. If it does, find such a circuit. If it does not, give an argument to show why no such circuit exist. 31. a 32. aWhat theorem helps identify or determine the existence of a Hamiltonian circuit on a connected graph? a. Hamiltonian Theorem b. Daren’s Theorem c. Eulerian Graph Theorem d. Dirac’s Theorem