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Graph Theory
Graph Theory Terms
12
Mathematics
Undergraduate 2
03/05/2008

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Term
Closed walk
Definition
When x=y and length>1
Term
Trail
Definition
When no edge is repeated in the x-y walk
Term
Circuit
Definition
A closed trail, when x=y and not edge is repeated
Term
Path
Definition
Whne no vertex occurs twice of a x-y walk
Term
Cycle
Definition
A closed path, when no vertex is repeated and x=y
Term
Connected
Definition

If there is a path between any two distinct vertices of G.

 

Only one component 

Term
k(G)
Definition
the number of components of G
Term
Multigraph
Definition
Let V be a finite nonempty set. We say that the pair(V,E) determines a multigraph G with vertex set V and edge set E if, for some x,y E V there are two or more edges in E or the form (x,y) or {x,y}
Term
Spanning Subgraph
Definition
If V1=V
Term
Induced Subgraph
Definition
If the subgraph contains all edges that are in orginal
Term
Complete graph
Definition
Denoted Kn  loop freee undirected graph where for all a,b E V a does not equal b there is an edge {a,b}
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