(a)
To define:
A tree.
Explanation of Solution
Definition: A tree is a connected undirected graph with no simple circuits. Because a tree cannot have a simple circuit, a tree cannot contain multiple edges or loops. Therefore any tree must be a simple graph.
An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices.
Example:
(b)
To define:
A forest.
Explanation of Solution
Definition: A forest is an undirected graph, all of whose connected components are trees.
i.e. the graph consists of a disjoint union of trees.
A forest is a disjoint union of trees, or equivalently anacyclic graph that is not necessarily connected.
Example:
An empty graph, a single tree and the discrete graph on a set of vertices are examples of forest tree.
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Chapter 11 Solutions
DISCRETE MATH.+ITS APPLICATIONS CUSTOM
- 1. Let F be a forest with 50 vertices and 35 edges. How many trees does have F. We need to quickly and urgently solve this question "arrow_forwarda. 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?arrow_forwardG is a forest with 100 vertices and 87 edges. How many additional edges should be added to make G a tree?arrow_forward
- How many lattice points does this line segment contain?arrow_forward2. Draw four spanning trees of graph G. C. d. We need to quickly and urgently solve this question "arrow_forwardConstruct a simple graph that is a forest with vertices B, C, D, E, F,G such that the degree of D is 2 and there are 2 components. What is the edge set? {DB,DC,EF,EG}arrow_forward
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