Why is question 7 on Mod 5 TBD?
Its simple in my opinion
Im doing the sols for a company and have it as follow
As it says it is a connected graph, there can be no isolated vertices, hence it must be a tree.
A) EDIT: Ooops. Accidentally subbed in the wrong values for Eulers formula. I stand corrected. v-e+f=2.
5-4+1=2
B) The graph only has one face. As a tree, there is only the undisclosed face which makes it one. Thus there is only 1 face. This is hence false
C) The variations of the tree that you can have mean that you can have an odd degree. I've drawn a few, but can't show it here. Therefore this is false.
D) The sum of the degrees must always be 8. With the fact that there are no loops, and the fact that they are all connected to each other, the first tree you draw will tell you the sum of the degrees, This is true
E) The graph cannot have a loop, otherwise, it is not a connected graph. There would be an isolated vertex, making this statement true
Therefore the number of true statements is equivalent to 3.
Answer is C.
Cowabunga dooods!