一些简单图论问题

延续以前呈上练习题的风格，所选的都是一些简单题目,错题，只是为了打好基础，那些较难的没有放上来。基本使用英文。
一些概念：

multigraph

• In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges[1]), that is, edges that have the same end nodes. Thus two vertices may be connected by more than one edge.

mixed graph

• A mixed graph G = (V, E, A) is a mathematical object consisting of a set of vertices (or nodes) V, a set of (undirected) edges E, and a set of directed edges (or arcs) A

Bigraph

• A bigraph (often used in the plural bigraphs) can be modelled as the superposition of a graph (the link graph) and a set of trees (the place graph).Each node of the bigraph is part of a graph and also part of some tree that describes how the nodes are nested. Bigraphs can be conveniently and formally displayed as diagrams.They have applications in the modelling of distributed systems for ubiquitous computing and can be used to describe mobile interactions. They have also been used by Robin Milner in an attempt to subsume Calculus of Communicating Systems (CCS) and π-calculus. They have been studied in the context of category theory.

begin:

1. The following graph is bipartite.
   

here , we want to show how to know a graph is bipartite or not.
just use the properties of the bigraph , color one part black and the other white. and we can list.
write program , for more , click here link.
we can easily know that if a subgraph of the original graph is isomorphic to C_k （k is odd）, then the original graph is not bipartite.
2. Which statements must be executed before S6 is executed in the program shown as below?

the answer:
S3,S1,S2,S4 simple
3. huffman code: What is the number of bits used by Huffman’s coding scheme to encode the English text “in mathematics and more specifically in graph theory a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense related the objects correspond to mathematical abstractions called vertices also called nodes or points and each of the related pairs of vertices is called an edge also called an arc or line typically a graph is depicted in diagrammatic form as a set of dots for the vertices joined by lines or curves for the edges graphs are one of the objects of study in discrete mathematics”.
answer: 2183.
then just write a little program , plant the little and beautiful tree， but we will note whether the space should be coded or not.
4. Find the length of a shortest path between a and z in the given weighted graph.

answer: 16. just write the program.
better question: loading…