*Studying for a chapter examination is a personal process, one which nobody else can do for you. Simply take the time to review what you have done. *

**Here are the new terms in Chapter 9. **

Arc [9.1]

Closed curve [9.3]

Connected graph [9.2]

Connected network [9.2]

Degree (vertex) [9.1]

Edge [9.1]

Euler circuit [9.1]

Euler’s circuit theorem [9.1]

Even vertex [9.1]

Four-color problem [9.3]

Fractal geometry [9.3]

Genus [9.3]

Graph [9.1]

Hamiltonian cycle [9.1]

Jordan curve [9.3]

Kruskal’s algorithm [9.2]

Loop [9.1]

Minimum spanning tree [9.2]

Network [9.1]

Number-of-edges theorem [9.2]

Odd vertex [9.1]

Operations research [Overview]

Planar curve [9.3]

Region [9.1]

Simple curve [9.3]

Sorted-edge method [9.1]

Spanning tree [9.2]

Tessellation [9.3]

Topologically equivalent [9.3]

Topology [9.3]

Traveling salesperson problem (TSP) [9.1]

Traversable network [9.1]

Tree [9.2]

Vertex [9.1]

Weight [9.2]

Weighted graph [9.2]

*If you can describe the term, read on to the next one; if you cannot, then look it up in the text (the section number is shown in brackets).*

**IMPORTANT IDEAS **

*Can you explain each of these important ideas in your own words?*

Konigsberg bridge problem [9.1]

Euler’s circuit theorem [9.1]

Hamiltonian cycles and the traveling salesperson problem (TSP) [9.1]

Kruskal’s algorithm [9.2]

Topologically equivalent figures, four-color problem, and fractals [9.3]

*Next, make sure you understand the types of problems in Chapter 9.*

**TYPES OF PROBLEMS **

Decide whether a network is an Euler circuit. [9.1]

Work floor-plan problems. [9.1]

Solve applied problems involving traversable networks. [9.1]

Determine whether a given graph is a tree. [9.2]

Find spanning trees for a given graph. [9.2]

Given a weighted graph, find the minimum spanning tree. [9.2]

Sort figures into topologically equivalent classes.[9.3]

Decide whether a given point is an interior or exterior point. [9.3]

Solve applied problems involving the four color-theorem. [9.3]

Design mosaics (tessellations). [9.3]

Once again, see if you can verbalize (to yourself) how to do each of the listed types of problems. Work all of **Chapter 9 Review Questions** (whether they are assigned or not).

Work through all of the problems before looking at the answers, and then correct each of the problems. The entire solution is shown in the answer section at the back of the text. If you worked the problem correctly, move on to the next problem, but if you did not work it correctly (or you did not know what to do), look back in the chapter to study the procedure, or ask your instructor. Finally, go back over the homework problems you have been assigned. If you worked a problem correctly, move on the next problem, but if you missed it on your homework, then you should look back in the text or talk to your instructor about how to work the problem. If you follow these steps, you should be successful with your review of this chapter.

We give all of the answers to the Chapter Review questions (not just the odd-numbered questions), so be sure to check your work with the answers as you prepare for an examination.