Identifying Spanning Trees
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Question 1 of 5
1. Question
Which of the following networks is NOT a spanning tree?Hint
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Categories of a Spanning Tree
`1.` Each `2` vertices only has one connection.`2.` Does not have any loops or cycles.`3.` Edges`=n-1`, where `n` is the number of vertices.
In other words, the number of edges is `1` less than the number of vertices.Check each network if they fit all the categories for a spanning tree.`1`st Figure
Each two vertices only has one connection and there are no loops or cycles in this network. It also has `5` edges- one less than the number of vertices, which is `6`.Therefore, this network is a spanning tree.`2`nd Figure
Notice that the three vertices at the top of the network creates a cycle, and spanning trees cannot have any loops or cycles.Therefore, this network is not a spanning tree.`3`rd Figure
Each two vertices only has one connection and there are no loops or cycles in this network. It also has `5` edges- one less than the number of vertices, which is `6`.Therefore, this network is a spanning tree.`4`th Figure
Each two vertices only has one connection and there are no loops or cycles in this network. It also has `5` edges- one less than the number of vertices, which is `6`.Therefore, this network is a spanning tree.Only the `2`nd figure is not a spanning tree.
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Question 2 of 5
2. Question
Which of the following networks is NOT a spanning tree?Hint
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Well Done!
Incorrect
Categories of a Spanning Tree
`1.` Each `2` vertices only has one connection.`2.` Does not have any loops or cycles.`3.` Edges`=n-1`, where `n` is the number of vertices.
In other words, the number of edges is `1` less than the number of vertices.Check each network if they fit all the categories for a spanning tree.`1`st Figure
Each two vertices only has one connection and there are no loops or cycles in this network. It also has `7` edges- one less than the number of vertices, which is `8`.Therefore, this network is a spanning tree.`2`nd Figure
Each two vertices only has one connection and there are no loops or cycles in this network. It also has `7` edges- one less than the number of vertices, which is `8`.Therefore, this network is a spanning tree.`3`rd Figure
Notice that there is a vertex that is not connected to the network, and this makes the number of edges only `6`, two less than the number of vertices, which is `8`.Therefore, this network is not a spanning tree.`4`th Figure
Each two vertices only has one connection and there are no loops or cycles in this network. It also has `6` edges- one less than the number of vertices, which is `7`.Therefore, this network is a spanning tree.Only the `3`rd figure is not a spanning tree.
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Question 3 of 5
3. Question
Which of the following is a spanning tree from the network below?
Hint
Help VideoCorrect
Great Work!
Incorrect
Categories of a Spanning Tree
`1.` Each `2` vertices only has one connection.`2.` Does not have any loops or cycles.`3.` Edges`=n-1`, where `n` is the number of vertices.
In other words, the number of edges is `1` less than the number of vertices.Check each network if they fit all the categories for a spanning tree.`1`st Figure
Notice that there are seven vertices that creates a cycle, and spanning trees cannot have any loops or cycles.Therefore, this network is not a spanning tree.`2`nd Figure
Notice that there are two vertices that is not connected, and vertices of a spanning trees should all be connected.Therefore, this network is not a spanning tree.`3`rd Figure
Notice that there are only eight vertices, and the given network has `9` vertices.Therefore, this network is not a spanning tree of the given network.`4`th Figure
Each two vertices are connected and there are no loops or cycles in this network. It also has `8` edges- one less than the number of vertices, which is `9`.Therefore, this network is a spanning tree.Only the `4`th figure is a spanning tree for the given network.
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Question 4 of 5
4. Question
Which of the following is a spanning tree from the network below?
Hint
Help VideoCorrect
Fantastic!
Incorrect
Categories of a Spanning Tree
`1.` Each `2` vertices only has one connection.`2.` Does not have any loops or cycles.`3.` Edges`=n-1`, where `n` is the number of vertices.
In other words, the number of edges is `1` less than the number of vertices.Check each network if they fit all the categories for a spanning tree.`1`st Figure
Each two vertices are connected and there are no loops or cycles in this network. It also has `7` edges- one less than the number of vertices, which is `8`.Therefore, this network is a spanning tree.`2`nd Figure
Notice that there are four vertices that is not connected, and vertices of a spanning trees should all be connected. This makes the network have `8` edges- the same count as that of its vertices.Therefore, this network is not a spanning tree.`3`rd Figure
Notice that there is a vertex that is not connected to the network and it makes the network have only `6` edges- two less than the number of vertices, which is `8`.Therefore, this network is not a spanning tree.`4`th Figure
Notice that there are only seven vertices, and the given network has `8` vertices.Therefore, this network is not a spanning tree of the given network.Only the `1`st figure is a spanning tree for the given network.
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Question 5 of 5
5. Question
Which of the following is a spanning tree from the network below?
Hint
Help VideoCorrect
Great Work!
Incorrect
Categories of a Spanning Tree
`1.` Each `2` vertices only has one connection.`2.` Does not have any loops or cycles.`3.` Edges`=n-1`, where `n` is the number of vertices.
In other words, the number of edges is `1` less than the number of vertices.Check each network if they fit all the categories for a spanning tree.`1`st Figure
Notice that there are only seven vertices, and the given network only has `6` vertices.Therefore, this network is not a spanning tree of the given network.`2`nd Figure
Notice that there are seven vertices that creates a cycle, and spanning trees cannot have any loops or cycles. This makes the network have `6` edges- the same count as that of its vertices.Therefore, this network is not a spanning tree.`3`rd Figure
Notice that there are two vertices that is not connected, and vertices of a spanning trees should all be connected.Therefore, this network is not a spanning tree.`4`th Figure
Each two vertices are connected and there are no loops or cycles in this network. It also has `5` edges- one less than the number of vertices, which is `6`.Therefore, this network is a spanning tree.Only the `4`th figure is a spanning tree for the given network.
Quizzes
- Vertices and Edges
- Degrees 1
- Degrees 2
- Degrees 3
- Drawing A Network 1
- Drawing A Network 2
- Completing a Table from a Network Diagram
- Network from Maps and Plans
- Identifying Paths and Cycles
- Eulerian Trails and Circuits 1
- Eulerian Trails and Circuits 2
- Identifying Spanning Trees
- Minimum Spanning Trees 1
- Minimum Spanning Trees 2
- Shortest Path 1
- Shortest Path 2