Why does this network meet the Euler's network formula?
As I was reading Fermat's Enigma, I encountered this graph below. The book says the graph meets the Euler's network formula, but I don't understand why there is a region at the top. If it's possible to add a region without two vertices, can't we control the number of regions just to meet the formula?
The graph
network
asked Dec 2 at 2:28
sflow
1
add a comment |
As I was reading Fermat's Enigma, I encountered this graph below. The book says the graph meets the Euler's network formula, but I don't understand why there is a region at the top. If it's possible to add a region without two vertices, can't we control the number of regions just to meet the formula?
The graph
network
asked Dec 2 at 2:28
sflow
1
Adding a loop adds one region and one edge, so $2-V+E-F$ is unchanged.
– bof
Dec 2 at 7:25
add a comment |
As I was reading Fermat's Enigma, I encountered this graph below. The book says the graph meets the Euler's network formula, but I don't understand why there is a region at the top. If it's possible to add a region without two vertices, can't we control the number of regions just to meet the formula?
The graph
network
asked Dec 2 at 2:28
sflow
1
As I was reading Fermat's Enigma, I encountered this graph below. The book says the graph meets the Euler's network formula, but I don't understand why there is a region at the top. If it's possible to add a region without two vertices, can't we control the number of regions just to meet the formula?
The graph
network
network
asked Dec 2 at 2:28
sflow
1
asked Dec 2 at 2:28
sflow
1
asked Dec 2 at 2:28
sflow
1
asked Dec 2 at 2:28
sflow
1
asked Dec 2 at 2:28
sflow
1
1
Adding a loop adds one region and one edge, so $2-V+E-F$ is unchanged.
– bof
Dec 2 at 7:25
add a comment |
Adding a loop adds one region and one edge, so $2-V+E-F$ is unchanged.
– bof
Dec 2 at 7:25
Adding a loop adds one region and one edge, so $2-V+E-F$ is unchanged.
– bof
Dec 2 at 7:25
Adding a loop adds one region and one edge, so $2-V+E-F$ is unchanged.
– bof
Dec 2 at 7:25
add a comment |
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Adding a loop adds one region and one edge, so $2-V+E-F$ is unchanged.
– bof
Dec 2 at 7:25