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Data Abstraction and Problem Solving with JAVA: Data Abstraction and Problem Solving with JAVA: Walls and MirrorsWalls and Mirrors GraphsGraphs

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Data Abstraction and Problem Solving with JAVA:

Data Abstraction and Problem Solving with JAVA:

Walls and Mirrors Walls and Mirrors

Carrano / Prichard Carrano / Prichard

Graphs

Graphs

(2)

An ordinary line graph

(3)

a) A campus map as a graph; b) a subgraph

(4)

Graphs that are a) connected; b) disconnected; and c) complete

(5)

a) A multigraph is not a graph; b) a self edge is not allowed in a graph

(6)

a) A weighted graph

(7)

b) A directed graph

(8)

a) A directed graph and b) its adjacency matrix

(9)

a) A weighted undirected graph and b) its adjacency matrix

(10)

a) A directed graph and b) its adjacency list

(11)

a) A weighted undirected graph and b) its adjacency list

(12)

Visitation order for a) a depth-first search; b) a breadth-first search

(13)

A connected graph with cycles

(14)

The results of a depth-first traversal,

beginning at vertex a, of the graph in

Figure 13-11

(15)

The results of a breadth-first traversal,

beginning at vertex a, of the graph in

Figure 13-11

(16)

A directed graph without cycles

(17)

The graph in Figure 13-14 arranged according to the topological orders a) a, g,

d, b, e, c, f and b) a, b, g, d, e, f, c

(18)

A trace of topSort1 for the graph in Figure 13-14

(19)

A trace of topSort1 for the graph in Figure 13-14

(20)

A trace of topSort2 for the graph in Figure 13-14

(21)

A spanning tree for the graph in Figure 13-11

(22)

Connected graphs that each have four vertices and three edges

(23)

The DFS spanning tree rooted at vertex a for the graph in Figure 13-11

(24)

The BFS spanning tree rooted at vertex a for the graph in Figure 13-11

(25)

A weighted, connected, undirected graph

(26)

A trace of PrimsAlgorithm for the graph in Figure 13-22,

beginning a vertex a

(27)

A trace of PrimsAlgorithm for the graph in Figure 13-22,

beginning a vertex a

(28)

A trace of PrimsAlgorithm for the graph in Figure 13-22,

beginning a vertex a

(29)

A trace of PrimsAlgorithm for the graph in Figure 13-22,

beginning a vertex a

(30)

A trace of PrimsAlgorithm for the graph in Figure 13-22,

beginning a vertex a

(31)

a) A weighted directed graph and b) its adjacency matrix

(32)

A trace of the shortest-path algorithm applied to the graph in Figure 13-24a

(33)

Checking weight[u] by examining the graph: a) weight[2] in Step 2;

b) weight[1] in Step 3

(34)

Checking weight[u] by examining the graph: c) weight[3] in Step 3;

b) weight[3] in Step 4

(35)

a) Euler’s bridge problem and b) its multigraph representation

(36)

Pencil and paper drawings

(37)

Connected undirected graphs based on the drawings in Figure 13-28

(38)

The steps to determine an

Euler circuit for the graph in

Figure 13-29b

(39)

The three utilities problem

(40)

Graphs for Self-Test Exercises 1, 2, and 3

(41)

A graph for Self-Test Exercises 6 and 7 and Exercises 1 and 3

(42)

A graph for Exercise 1

(43)

A graph for Exercises 3 and 8

(44)

Graphs for Exercises 5 and 6

(45)

A graph for Exercise 11

(46)

A graph for Exercise 13

References

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