《离散数学》杨争锋ch08-1
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Example: See Figure 2 (page 590)
(3) Definition 3 (page 590) A pseudograph G=(V, E) consists of a set
V of vertices, a set E of edges, and a function f from E to { {u,v} | u,v∈V }. An edge is a loop if f(e)={u,u}={u} for some u∈V.
§9.1 Introduction to Graphs 1. Types of Graphs (1) Definition 1 (page 589)
A simple graph G=(V,E) consists of V, a nonempty set of vertices (顶点), and E, a set of unordered pairs of distinct elements of V called edges.
Chapter 9 Graphs §9.1 Introduction to Graphs §9.2 Graph Terminology §9.3 Representing Graphs and Graph
Isomorphism §9.4 Connectivity §9.5 Euler and Hamilton Paths §9.6 Shortest-Path Problems §9.7 Planar Graphs §9.8 Graph Coloring
Example: See Figure 5 (page 591).
(6) Summary (Graph Terminole Graph Multigraph Pseudograph Directed graph Directed multigraph
Edges Multiple Edge? Loops?
Undirected No
No
Undirected Yes
No
Undirected Yes
Yes
Directed
No
Yes
Directed
Yes
Yes
Example: See Figure 3 (page 590).
(4) Definition 4 (page 591) A directed graph G=(V, E) consists of
a set of vertices V and a set of edges E that are ordered pairs of elements of V.
Remark: the edge from u to v-------(u,v)
Example: See Figure 4 (page 591).
(5) Definition 5 (page 591) A directed multigraph G=(V, E)
consists of a set V of vertices, a set E of edges, and a function f from E to { (u,v) | u, v∈V }. The edges e1 and e2 are multiple edges if f(e1)=f(e2).
Example: See Figure 1 (page 590).
(2) Definition 2 (page 590) A multigraph G=(V,E) consists of a set V
of vertices, a set E of edges, and a function from E to { {u,v} | u,v ∈V, u≠v}. The edges e1 and e2 are called multiple or parallel edges if f(e1)=f(e2).
(3) Definition 3 (page 590) A pseudograph G=(V, E) consists of a set
V of vertices, a set E of edges, and a function f from E to { {u,v} | u,v∈V }. An edge is a loop if f(e)={u,u}={u} for some u∈V.
§9.1 Introduction to Graphs 1. Types of Graphs (1) Definition 1 (page 589)
A simple graph G=(V,E) consists of V, a nonempty set of vertices (顶点), and E, a set of unordered pairs of distinct elements of V called edges.
Chapter 9 Graphs §9.1 Introduction to Graphs §9.2 Graph Terminology §9.3 Representing Graphs and Graph
Isomorphism §9.4 Connectivity §9.5 Euler and Hamilton Paths §9.6 Shortest-Path Problems §9.7 Planar Graphs §9.8 Graph Coloring
Example: See Figure 5 (page 591).
(6) Summary (Graph Terminole Graph Multigraph Pseudograph Directed graph Directed multigraph
Edges Multiple Edge? Loops?
Undirected No
No
Undirected Yes
No
Undirected Yes
Yes
Directed
No
Yes
Directed
Yes
Yes
Example: See Figure 3 (page 590).
(4) Definition 4 (page 591) A directed graph G=(V, E) consists of
a set of vertices V and a set of edges E that are ordered pairs of elements of V.
Remark: the edge from u to v-------(u,v)
Example: See Figure 4 (page 591).
(5) Definition 5 (page 591) A directed multigraph G=(V, E)
consists of a set V of vertices, a set E of edges, and a function f from E to { (u,v) | u, v∈V }. The edges e1 and e2 are multiple edges if f(e1)=f(e2).
Example: See Figure 1 (page 590).
(2) Definition 2 (page 590) A multigraph G=(V,E) consists of a set V
of vertices, a set E of edges, and a function from E to { {u,v} | u,v ∈V, u≠v}. The edges e1 and e2 are called multiple or parallel edges if f(e1)=f(e2).