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Fundamentals of Graph
Fundamentals of Graph
Theory
Theory
Chapter 3
Artemio P. Magabo
Artemio P. Magabo
Professor of Electrical Engineering
Department of Electrical and Electronics Engineering
University of the Philippines  Diliman
Department of Electrical and Electronics Engineering
Topology
Topology
is a branch of geometry that concerns
with the properties of a geometric figure that are
not changed when the figure is twisted, bent,
folded, stretched or tied in knots, provided that no
parts of the figure are cut apart or joined together.
A
graph
is a picture of an electric circuit where
each element has been replaced by a line segment.
3
Ω
4V
+

2A
+

V
x
+

5V
x
1
Ω
2
Ω
Department of Electrical and Electronics Engineering
Definitions
Node
– a point of connection of two or more
elements
Path
 a set of elements that may be traversed in
order without passing through the same node
twice
Branch
 a single path, containing one simple
element, which connects one node to another
node
Loop
 a closed path
Mesh
 a loop which does not contain any other
loop within it
Department of Electrical and Electronics Engineering
Subgraph
– the graph formed after some
branches are removed from the original graph
Planar Graph
 a graph which may be drawn on a
plane surface in such a way that no branch
passes over or under any other branch
Nonplanar Graph
 a graph which is not planar
These planar graphs are topologically equivalent.
d
b
c
a
c
b
d
a
a
c
d
b
n=4
b=6
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n=6
b=9
This graph is nonplanar.
n=5
b=9
This graph is planar.
Department of Electrical and Electronics Engineering
Tree
 a subgraph with the following properties:
1. It contains all the nodes of the original
graph. No node is left in isolation.
2. It contains (n1)
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This note was uploaded on 01/13/2011 for the course EEEI 33 taught by Professor Co during the Winter '10 term at University of the Philippines Diliman.
 Winter '10
 Co

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