(a) Consider the following graph.ad90gbh(i) Explain giving reason for your answer, why an Euler circuit exists. Indicate the Eulercircuit.(ii) Determine a Hamilton circuit for the graph.(b) Draw the complete bipartite graph, K3,5.

Answered: Image /qna-images/answer/179c7bdc-ac95-46c9-bb48-d06dcca22d63.jpg

Answered: (a) Consider the following graph. a d…

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter14: Numerical Methods

Section14.1: Introduction To Root Finding

Problem 1E

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6) Consider the graph at the right: b. a. (5 pts) Does it have an Euler circuit? (5 pts) Does it have an Euler path? c. (5 pts) Does it have a Hamilton circuit? d. (5 pts) Does it have a Hamilton path? 1 2 4 K 6 7 9 10 11 12 3 13 00 8
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(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.
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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)
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8. (a) Find the chromatic number x of the 9-vertex graph below. Explain. (b) Find the edge chromatic number x' of the graph below. Explain. А B D O F E I H. (c) Does this graph have a Hamiltonian cycle? If so, list the vertices in order of such cycle. If not, explain why not. (d) Does this graph have an Euler circuit? If so, explain how you know. If not, does it have an Euler path? If so, explain how you know. Include a drawing of this graph in your solution.

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(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.