* Graph property http://en.wikipedia.org/wiki/Graph_property
graph property or graph invariant
thay depends only on the abstract structure
** Definitions
goal: focus on the abstract structure of graphs
describe: be a property preserved under all possible isomorphisms of a graph
graph invariant: for properties expressed quantitatively
_eg: the number of vertices of degree 1 in a graph
property: descriptive characterizations(特性) of graphs
_eg: graph does not have vertices of degree 1 (is used to describe a class of graph)
a graph property is a class of graphs, with the property that any two isomorphic graphs either both belong to the class, or both do not belong to it
indicator function: test a graph is in the class of not. return true, if a graph in the class, return false, if it is not
** Properties of propertie
property classes
hereditary:
* Subgraphs
contains part of the graph, both vertex and adjacency relation(edge)
G's isomorphic is G's subgraph. G is G's subgraph?
G's spanning subgraph of factor: has same vertex set
induced subgraph:
H = (V1,E1), G = (V,E), H is subgraph of E,
all the edges between the vertices in V1 from E are in E1
(for all vertices in V1, if the two vertices have edge in E, the E1 much has an edge)
describe: if for any pair of vertices x and y of H,
_ xy is an edge of H if and only if xy is an edge of G
* source
百度百科 http://baike.baidu.com/view/79350.htm?fr=aladdin
Glossary of graph theory http://en.wikipedia.org/wiki/Induced_subgraph
Graph intro,has induce graph, and has example https://courses.cit.cornell.edu/info2950_2012sp/graph.pdf