3.3. Edges=n-1=n−1, where nn is the number of vertices.
In other words, the number of edges is 11 less than the number of vertices.
Check each network if they fit all the categories for a spanning tree.
11st Figure
Each two vertices only has one connection and there are no loops or cycles in this network. It also has 55 edges- one less than the number of vertices, which is 66.
Therefore, this network is a spanning tree.
22nd 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.
33rd Figure
Each two vertices only has one connection and there are no loops or cycles in this network. It also has 55 edges- one less than the number of vertices, which is 66.
Therefore, this network is a spanning tree.
44th Figure
Each two vertices only has one connection and there are no loops or cycles in this network. It also has 55 edges- one less than the number of vertices, which is 66.
Therefore, this network is a spanning tree.
Only the 22nd figure is not a spanning tree.
Question 2 of 5
2. Question
Which of the following networks is NOT a spanning tree?
3.3. Edges=n-1=n−1, where nn is the number of vertices.
In other words, the number of edges is 11 less than the number of vertices.
Check each network if they fit all the categories for a spanning tree.
11st Figure
Each two vertices only has one connection and there are no loops or cycles in this network. It also has 77 edges- one less than the number of vertices, which is 88.
Therefore, this network is a spanning tree.
22nd Figure
Each two vertices only has one connection and there are no loops or cycles in this network. It also has 77 edges- one less than the number of vertices, which is 88.
Therefore, this network is a spanning tree.
33rd Figure
Notice that there is a vertex that is not connected to the network, and this makes the number of edges only 66, two less than the number of vertices, which is 88.
Therefore, this network is not a spanning tree.
44th Figure
Each two vertices only has one connection and there are no loops or cycles in this network. It also has 66 edges- one less than the number of vertices, which is 77.
Therefore, this network is a spanning tree.
Only the 33rd figure is not a spanning tree.
Question 3 of 5
3. Question
Which of the following is a spanning tree from the network below?
3.3. Edges=n-1=n−1, where nn is the number of vertices.
In other words, the number of edges is 11 less than the number of vertices.
Check each network if they fit all the categories for a spanning tree.
11st 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.
22nd 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.
33rd Figure
Notice that there are only eight vertices, and the given network has 99 vertices.
Therefore, this network is not a spanning tree of the given network.
44th Figure
Each two vertices are connected and there are no loops or cycles in this network. It also has 88 edges- one less than the number of vertices, which is 99.
Therefore, this network is a spanning tree.
Only the 44th figure is a spanning tree for the given network.
Question 4 of 5
4. Question
Which of the following is a spanning tree from the network below?
3.3. Edges=n-1=n−1, where nn is the number of vertices.
In other words, the number of edges is 11 less than the number of vertices.
Check each network if they fit all the categories for a spanning tree.
11st Figure
Each two vertices are connected and there are no loops or cycles in this network. It also has 77 edges- one less than the number of vertices, which is 88.
Therefore, this network is a spanning tree.
22nd 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 88 edges- the same count as that of its vertices.
Therefore, this network is not a spanning tree.
33rd Figure
Notice that there is a vertex that is not connected to the network and it makes the network have only 66 edges- two less than the number of vertices, which is 88.
Therefore, this network is not a spanning tree.
44th Figure
Notice that there are only seven vertices, and the given network has 88 vertices.
Therefore, this network is not a spanning tree of the given network.
Only the 11st figure is a spanning tree for the given network.
Question 5 of 5
5. Question
Which of the following is a spanning tree from the network below?
3.3. Edges=n-1=n−1, where nn is the number of vertices.
In other words, the number of edges is 11 less than the number of vertices.
Check each network if they fit all the categories for a spanning tree.
11st Figure
Notice that there are only seven vertices, and the given network only has 66 vertices.
Therefore, this network is not a spanning tree of the given network.
22nd 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 66 edges- the same count as that of its vertices.
Therefore, this network is not a spanning tree.
33rd 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.
44th Figure
Each two vertices are connected and there are no loops or cycles in this network. It also has 55 edges- one less than the number of vertices, which is 66.
Therefore, this network is a spanning tree.
Only the 44th figure is a spanning tree for the given network.