## Integral 3 years ago Sigh let's try this again: Let G be a connected regular graph with n edges. How many vertices can G have?

1. Integral

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.

2. benice

the most vertices it can have is n-1

3. Integral

4. benice

sorry n+1

5. benice

actual the graph is regular so it n

6. benice

the min would be a fully connected graph

7. benice

|dw:1332551750259:dw|

8. Integral

|dw:1332551852360:dw|

9. Integral

Doesn't regular mean no loops or repeated edges?

10. benice

see i dont think that graph is regular a regular means each vertex has the same number of edges as every other vertex

11. Integral

Ohhh

12. Integral

So a regular connected graph would have to be a cycle if the number of vertices is greater than 2?

13. Integral

a simple graph whose vertices all have the same degree r.

14. Integral

Yes you're right.

15. benice

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

16. benice

5 vertices fully connected is 10 6 vertices ..... 15 .. so

17. Integral

wait you lost me

18. benice

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

19. benice

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

20. benice

sorry about the confusion in technical terms it's been a while

21. benice

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