1. Graph Theory & Networks Name:____________Date:______ Try to trace each figure below without lifting your pencil from the paper and without retracing any of the segments or arcs. If you can trace a figure without lifting the pencil off of the page & tracing each segment or arc exactly once then the figure is called _________________. These figures are called ____________________ or ______________________. The segments or curves are called _______________. Their endpoints are called _________________or _______________. The nodes can be ____________ or ____________. Count the number of arcs which have that vertex or node as an endpoint. If a graph ____________________________________, then it is not traversable 1.

2. 3. 4. 2.

3. 5. Create a network for each description a. Traversable with 4 nodes, 5 arcs b. Nontraversable with 5 nodes, 7 arcs 6. Have a look at the house plan below, with five rooms and sixteen doors in total. The intention is to make a run through the rooms and pass each of the sixteen doors exactly once. What is the route to run? 7. There are three houses (A, B, and C) and three utilities (gas (G), water (W), and electricity (E)). Each house must get a direct, uninterrupted connection to each utility, but the various connections should not cross each other. How can the connections be made?