True or False. Justify if answer is False. Give a counter example or a proof or well-writtenjustification.1. Every acyclic graph has a spanning forest.2. The following graph is not bipartite. Label the vertices.3.4.Every tree is a path.Every tree is a forest.

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Answered: True or False. Justify if answer is…

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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When a vertex Q is connected by an edge to a vertesx K, what is the term for the relationship between Q and K A. Q and K are "isolated" B. Q and K are adjacent C. Q and K are "insecure" D. Q and K are "incident"
14. Answer the following about trees. Explain your answers. You will not be awarded any credit for simply writing a number: (a) If T is a spanning tree of the graph K9, how many edges are in T? (b) If S is a tree on n vertices, what is the total degree of S? Hint: your answer should be in terms of n. (c) A forest F consists of twelve trees, each having 5 vertices. What is the total degree of F ?
Which of the following statements about a connected graph is always TRUE? A path of edges exists between any two vertices of the graph. There is an even number of vertices on the graph. There is an even number of edges on the graph. Every pair of vertices is joined by a single edge.
Answer the following questions: a.Suppose that a connected bipartite planar simple graph has e edges and v vertices. Show that e ≤ 2v − 4if v ≥ 3. b. Let G be a graph with n − 1 edges. Show that the following three statements are equivalent:(i) G is connected(ii) G is acyclic;(iii) G is a tree.
12) True or False. Points A and L are corresponding vertices, points B and M are corresponding vertices, points C and N are corresponding vertices, and points D and O are corresponding vertices.
(a) What is the degree of vertex E ? (b) List all the even vertices and all the odd vertices.Click on "None" as needed. List of the even vertices: List of the odd vertices: (c) List all vertices that are adjacent to vertex D .Click on "None" as needed.
Let H be the graph below: (a) How many trees, with vertex set [7], have H as a subgraph? (b) How many graphs, with vertex set [n] and n > 7, have H as a subgraph? (c) How many graphs, with vertex set [n] and n > 7, have H as an induced subgraph? (d) How many trees, with vertex set [n] and n > 7, have H as a subgraph? Hint: Moon’s theorem (e) How many trees, with vertex set [n] and n > 7, have H as an induced subgraph?
a. Given a forest consisting of 3 trees and 20 vertices. how many edges are there? b. Given a forest consisting of 5 trees and 20 edges. how many vertices are there?

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True or False. Justify if answer is False. Give a counter example or a proof or well-written justification. 1. 2. The following graph is not bipartite. Label the vertices. 3. Every acyclic graph has a spanning forest. 4. Every tree is a path. Every tree is a forest.