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Chapter 14: Problem 48

Describe how to obtain a spanning tree for a connected graph.

Short Answer

Expert verified
To obtain a spanning tree for a connected graph, begin by selecting any edge. Then, add more edges that connect a new vertex to this subgraph, ensuring no cycles are formed. Repeat this process until all vertices from the original graph are included in the subgraph which then becomes the spanning tree.

Step by step solution

01

Identify the vertices

In the given graph, identify all the vertices. Any spanning tree must contain all of these vertices, therefore the first task is to identify every vertex within the graph.
02

Select an edge

Select a specific edge to start forming the subgraph. This initial edge will act as starting point for the spanning tree.
03

Add edges

Proceed by adding more edges to the initial one, while ensuring that no cycles are formed. One way to do this is to always connect an edge that involves a new vertex to the current subgraph.
04

Continue until all vertices are included

Continue adding edges without forming cycles until all the vertices are included in the subgraph. This subgraph is now the spanning tree of the original graph.

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Most popular questions from this chapter

How can you look at a graph and determine if it has a Hamilton circuit?

Group members should determine a relationship that exists among some, but not all, members. Did some of you know one another before the course began? Do some of you have the same academic major? Be as creative as possible in determining this relationship. Then create a graph that serves as a model for describing this relationship.

Describe a situation involving relationships that can be modeled with a graph.

In Exercises 5-6, draw two equivalent graphs for each description. The vertices are \(A, B, C\), and \(D\). The edges are \(A D, B C, D C\), \(B B\), and \(D B\).

Describe how to determine the number of Hamilton circuits in a complete graph.
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