Unformatted text preview: Paths
Path
sequence of alternating
vertices and edges
begins with a vertex
ends with a vertex V a each edge is preceded and
followed by its endpoints Simple path P1
d U
c path such that all its vertices
and edges are distinct Examples b
X P2 h Z e
W g
f P1=(V,b,X,h,Z) is a simple path Y P2=(U,c,W,e,X,g,Y,f,W,d,V) is a
path that is not simple
CSE 2011
Prof. J. Elder 6 Last Updated: 4/1/10 10:16 AM Cycles
Cycle
circular sequence of alternating
vertices and edges
each edge is preceded and
followed by its endpoints a Simple cycle
cycle such that all its vertices
and edges are distinct U b d X C2
e c Examples C2=(U,c,W,e,X,g,Y,f,W,d,V,a, )
is a cycle that is not simple 7 h Z C1 W C1=(V,b,X,g,Y,f,W,c,U,a, ) is a
simple cycle CSE 2011
Prof. J. Elder V g
f
Y Last Updated: 4/1/10 10:16 AM Subgraphs
A subgraph S of a graph
G is a graph such that
The vertices of S are a
subset of the vertices of G
Subgraph The edges of S are a
subset of the edges of G A spanning subgraph of
G is a subgraph that
contains all the vertices of
G
Spanning subgraph
CSE 2011
Prof. J. Elder 8 Last Updated: 4/1/10 10:16 AM Connectivity
A graph is connected if
there is a path between
every pair of vertices
A connected component
of a graph G is a maximal
connected subgraph of G Connected graph Non connected graph with two
connected components
CSE 2011
Prof. J. Elder 9 Last Updated: 4/1/10 10:16 AM Trees Tree Forest Graph with Cycle A tree is a connected, acyclic, undirected graph.
A forest is a set of trees (not necessarily connected)
CSE 2011
Prof. J. Elder  10  Last Updated: 4/1/10 10:16 AM ...
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 Fall '11
 Elder
 Graph Theory, Data Structures, Planar graph, Glossary of graph theory, Prof. J., Prof. J. Elder

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