Discrete Mathematics for Computer Science

Connected Graphs 357 contradicts the assumption that a vertex such as w exists. Therefore, the algorithm is exe- cuted for each ...

358 CHAPTER 6 Graph Theory Maude, Harold, George, and Elizabeth if a breadth first search was used. Even the Job Assignment Prob ...

Connected Graphs 359 INPUT: Connected graph G = (V, E), and start vertex v0 RESULT: Each vertex and each edge is examined Create ...

360 CHAPTER 6 Graph Theory INPUT: Graph G = (V, E) OUTPUT: For each vertex, a number labeling its connected component Create an ...

The K6nigsberg Bridge Problem 361 A breadth first search could also be used to find the connected components of a graph. The com ...

362 CHAPTER 6 Graph Theory be difficult, but it would require that the terminology of multigraphs be explained. The notions are ...

The Kbnigsberg Bridge Problem 363 of vertex 1 so there is an addition of two to the degree of vertex 1 for these occurrences. A ...

364 CHAPTER 6 Graph Theory 12 8 3 69 4 10 G (^1 8 8) 1*2 7 (^36 39) 4° •- 010 51 90 (^4 5 11) T u H Figure 6.28 Circuit that is ...

The K6nigsberg Bridge Problem 365 6.8.1 Graph Tracing In directing a plotting device, commands are given to indicate where a pen ...

366 CHAPTER 6 Graph Theory After deleting the remaining edges that were added to G to form H, k edge-disjoint trails containing ...

Exercises 367 W Exercises Construct connected graphs of the following sorts: (a) All graphs of five vertices with at least seve ...

368 CHAPTER 6 Graph Theory Draw the depth first search tree or the breadth first search tree that results from the following: (a ...

Exercises 369 The Hall of Horrors at an amusement park challenges you to enter at the Start door and find your way to the Escap ...

370 CHAPTER 6 Graph Theory Find a tracing that minimizes the number of pen lifts for the graph shown. 12 13 14 NA L 1 11 TO 9 ...

Trees 371 H H H H HH H H H C H H CC H H H C C H H C H H H C Methane H c-.H H Ethane H C H C H H H1 Butane Isobutane (a) Cayley's ...

372 CHAPTER 6 Graph Theory n=1 n=2 n=3 n=4 n=5 Figure 6.34 Trees with five or fewer vertices. 6.10.2 Characterization of Trees B ...

Trees 373 T is acyclic and the addition of any edge joining two nonadjacent vertices creates a cycle. Proof. (1 =. 2) The proo ...

374 CHAPTER 6 Graph Theory Theorem 2. Let T be a graph. T is a tree if and only if any two vertices of T are joined by a unique ...

Spanning Trees 375 INPUT: Connected graph G = (V, E) OUTPUT: A spanning tree T of G V(T) = V(G) /* Initialize */ E(T) = 0 for ea ...

376 CHAPTER 6 Graph Theory 6.11.3 Kruskal's Algorithm for Weighted Graphs Figure 6.36 shows a graph that models a communication ...