anonymous
  • anonymous
Sigh let's try this again: Let G be a connected regular graph with n edges. How many vertices can G have?
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
A graph which is connected in the sense of a topological space, i.e., there is a path from any point to any other point in the graph.
anonymous
  • anonymous
the most vertices it can have is n-1
anonymous
  • anonymous
Can you post your reasoning please?

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anonymous
  • anonymous
sorry n+1
anonymous
  • anonymous
actual the graph is regular so it n
anonymous
  • anonymous
the min would be a fully connected graph
anonymous
  • anonymous
|dw:1332551750259:dw|
anonymous
  • anonymous
|dw:1332551852360:dw|
anonymous
  • anonymous
Doesn't regular mean no loops or repeated edges?
anonymous
  • anonymous
see i dont think that graph is regular a regular means each vertex has the same number of edges as every other vertex
anonymous
  • anonymous
Ohhh
anonymous
  • anonymous
So a regular connected graph would have to be a cycle if the number of vertices is greater than 2?
anonymous
  • anonymous
a simple graph whose vertices all have the same degree r.
anonymous
  • anonymous
Yes you're right.
anonymous
  • anonymous
for a fully connected is regular as each vertix has the max number of edges so for a given number of vertices ie t the number of edges (t)(t-1)/2
anonymous
  • anonymous
5 vertices fully connected is 10 6 vertices ..... 15 .. so
anonymous
  • anonymous
wait you lost me
anonymous
  • anonymous
there is a min and the max .. .we got the max ... the min is a fully connected graph so if we were give 10 edges |dw:1332552333694:dw| we know it has 5 vertice but what would happen if we had 14 edges
anonymous
  • anonymous
for n edges the degree count is n*2 so the max is n*2/2 and the min is the number which leaves no remainder n*2/deg(x) x regular grpah
anonymous
  • anonymous
sorry about the confusion in technical terms it's been a while
anonymous
  • anonymous
so if we had 15 edges the toatal degrees would be 30 the max number of vertices is 15 with each degree 2 the min would be 6vertices with each degree 5

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