By W. D. Wallis

Concisely written, mild creation to graph concept appropriate as a textbook or for self-study Graph-theoretic functions from various fields (computer technological know-how, engineering, chemistry, administration technological know-how) second ed. contains new chapters on labeling and communications networks and small worlds, in addition to accelerated beginner's fabric Many extra adjustments, advancements, and corrections due to school room use

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**Extra info for A Beginner's Guide to Graph Theory**

**Example text**

MN would complete a cycle of length 3 (too short), so the only other choices are MS and NS, forming route EMSNE (or ENSME) at a cost of $530. 6 The Traveling Salesman Problem 41 In this example, the best route is ENMSE, with cost $510, and it does not arise from the nearest neighbor algorithm, no matter which starting vertex is used. 1 How many different Hamilton cycles are there in K v ? a a b b a f g g h b c a b c c d g e f h g h Fig. 19. 19, find all Hamilton cycles. 3 Solve the Traveling Salesman Problem for the following graphs by finding all their Hamilton cycles.

Ab = 24 ae = 23 ad = 20 ae = 21 be = 27 (iii) bd = 22 be = 30 cd = 26 ee = 27 de = 28. (iv) ab = 24 ae = 22 ad = 30 ae = 29 be = 17 bd = 19 be = 30 cd = 18 ee = 21 de = 25. 4, find the routes generated by the nearest neighbor algorithm starting at each of the five vertices in turn. 4 for the following lists of costs. (i) ab = 59 ae = 69 ad = 60 ae = 58 be = 56 bd = 69 be = 54 cd = 58 ee = 66 de = 61. (ii) ab = 16 ae = 24 ad = 30 ae = 48 be = 27 bd = 29 be = 44 cd = 16 ee = 46 de = 51. (iii) ab = 91 ae = 79 ad = 75 ae = 82 be = 87 bd = 64 be = 78 cd = 68 ee = 81 de = 88.

We say that two vertices are connected when there is a walk joining them. ") Two vertices of G are connected if and only if they lie in the same component of G; G is a connected graph if and only if all pairs of its vertices are connected. ) If vertices x and yare connected, then their distance D(x, y) is the length of the shortest path joining them; by definition D(x, x) = O. Example. 1, there are several paths from b to h: bcdh, bch, bgdh, bgdch, befgdh and befgdch. The shortest is bch, of length 2, so D(b, h) = 2.