7. We define a forest to be a graph with no cycles. a. Explain why this is a good name. That is, explain why a forest is a union of trees. b. Suppose F is a forest consisting of m trees and v vertices. How many edges does F have? Explain. c. Prove that any graph G with v vertices and e edges that satisfies v

7. We define a forest to be a graph with no cycles. a. Explain why this is a good name. That is, explain why a forest is a union of trees. b. Suppose F is a forest consisting of m trees and v vertices. How many edges does F have? Explain. c. Prove that any graph G with v vertices and e edges that satisfies v

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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For which of the following does there exist a simple graph G = - (V, E) satisfying the specified conditions? Select one: O A. It has 7 vertices, 10 edges, and more than two components. B. It has 8 vertices, 8 edges, and no cycles. O C. It has 6 vertices, 11 edges, and more than one component. O D. It is connected and has 10 edges, 5 vertices and fewer than 6 cycles. O E. It has 3 components, 20 vertices and 16 edges.
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1 (2.2.3). Find the number of spanning trees of the following graph.
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Show all possible connected sub graphs of the following graph. How many of them are there refer to image below
Let G be graph with 8 vertices and 10 edges. If every vertex of G has degree 2 or 3, then How many vertices of each degree does G have? Select the correct response: A. G has 1 vertices of degree 2 and 7 vertices of degree 3. B. G has 2 vertices of degree 2 and 6 vertices of degree 3. C. G has 3 vertices of degree 2 and 5 vertices of degree 3. D. G has 4 vertices of degree 2 and 4 vertices of degree 3. E. G has 5 vertices of degree 2 and 3 vertices of degree 3. F. G has 6 vertices of degree 2 and 2 vertices of degree 3. G. G has 7 vertices of degree 2 and 1 vertices of degree 3. H. G has 8 vertices of degree 2 and 0 vertices of degree 3. I. No such graph exists.
Construct a graph with vertices I, J, K, L, M, N that has an Euler path, the degree of K is 1 and the degree of N is 3. What is the edge set? ←
Need just correct option.
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Refer to the accompanying graph. Complete parts (a) through (c) in order. Starting at A, the circuit is Starting at B, the circuit is Starting at C, the circuit is Starting at D, the circuit is Starting at E, the circuit is (Simplify your answers.) (b) Which of the circuits for M A. The circuit that stai TL-- AL - and the total weight is otal weight is otal weight is otal weight is otal weight is A D C E→B→A A B C D→E→A A C D E→B→A ... A-E→C D→B→A B 13 15 60 C (a) Use the nearest neighbor algorithm starting at each of the vertices in turn to determine an approximate solution to the problem of finding a minimum Hamilton circuit for the graph. In each case, find the total weight of the circuit. 6/ 57 14 9 8 E 12 D ion to the problem of finding a minimum Hamilton circuit for the graph? Select all that apply.