46.9 Discrete

9. Let G be a graph. Prove that....

46.11 Discrete

11. Let G be a graph with... (see attached)

48.1 Discrete

1. We noticed that a graph with more than two vertices of odd degree cannot have an Eulerian trail... (see attached).

48.2 Discrete

2. A domino is a 2x1 rectangular piece of wood. On each half of the domino is a number, denoted by dots. In the figure, we show all C(5,2) = 10 dominoes we can make where the numbers on the dominoes are all pairs of values chosen from {1,2,3,4,5} (we do not include dominoes where the two numbers are the same)... (Please see attachment for full question.)

48.3 Discrete

Let G be a connected graph that is not Eulerian. Prove that it is possible to add a single vertex to G together with some edges from this new vertex to some old vertices so that the new graph is Eulerian. Please see attachment for background and hints.