Graph Theory,Graph Terminologies,Planar Graph & Graph Colouring
Interaksi 3 Graph Theory
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Transcript of Interaksi 3 Graph Theory
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7/28/2019 Interaksi 3 Graph Theory
1/12
Discrete Math by R.S. Chang, Dept. CSIE, NDHU 1
IPG KAMPUS IPOH
Program Pensiswazahan Guru
MTE3104 Matematik Keputusan
INTERAKSI 3
An Introduction to Graph Theory
oleh
En Murugiah & Cik Tang Swee Khuan
diadaptasi dari
Discrete Maths by R.S. Chang
Dept CSIE, NDHU
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Discrete Math by R.S. Chang, Dept. CSIE, NDHU 2
Pregel
River
Kneipkof
Island
New Pregel River
Old Pregel River
a
b
c
d
Find a way to walk about the city so as to cross
each bridge exactly once and then return to the
starting point.
The Seven Bridges of Konigsberg
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Discrete Math by R.S. Chang, Dept. CSIE, NDHU 3
Definitions and Examples
Undirected graph Directed graph
isolated vertex
adjacent
Loop
(GELUNG)
multiple
edges
simple graph (GRAF RINGKAS): an undirected graph without loop
or multiple edgesDegree/order (DARJAH/PERINGKAT) of a vertex: number of
edges connected
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Discrete Math by R.S. Chang, Dept. CSIE, NDHU 4
Definitions and Examples
x y
walk: no restriction
a-b-d-a-b-c
path: no vertex can be repeateda-b-c-d-e
trail: no edge can be repeated
a-b-c-d-e-b-d
closed ifx=y
closed path: cycle (KITAR) (a-b-c-d-a)
a
b
c
d
e
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Discrete Math by R.S. Chang, Dept. CSIE, NDHU 5
Definitions and Examples
degree/order of a vertex
is the number of edges
Incident on it
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Discrete Math by R.S. Chang, Dept. CSIE, NDHU 6
Definitions and Examples
A simple graph (GRAF RINGKAS): no loops, no more thanone edge (SISI) connecting any pair of vertices
A walk: a sequence of edges in which the end of one edge
(except the last) is the beginning of the next
A trail is a walk in which no edge is repeated
A path is a trail in which no vertex is repeated
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7/28/2019 Interaksi 3 Graph Theory
7/12Discrete Math by R.S. Chang, Dept. CSIE, NDHU 7
Definitions and Examples
An incidence matrix is a way of representing graph bymatrix.
D
A B
C
A B C D
A 0 1 2 1
B 1 0 1 0
C 2 1 0 1
D 1 0 1 0
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7/28/2019 Interaksi 3 Graph Theory
8/12Discrete Math by R.S. Chang, Dept. CSIE, NDHU 8
a
b
d
e
disconnected withtwo components
a
b
c
d
e
Connected graph
Definitions and Examples
c
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7/28/2019 Interaksi 3 Graph Theory
9/12Discrete Math by R.S. Chang, Dept. CSIE, NDHU 9
A complete graph is a simple graph in
which every pair of vertices isconnected by an edge
a
b
c
d
e
K5
Definitions and Examples
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7/28/2019 Interaksi 3 Graph Theory
10/12Discrete Math by R.S. Chang, Dept. CSIE, NDHU 10
Planar Graphs
A graph (or multigraph) G is calledplanarifG can bedrawn in the plane with its edges intersecting only at vertices ofG.
K4 K5
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11/12Discrete Math by R.S. Chang, Dept. CSIE, NDHU 11
Planar Graphs
Bipartite graph and complete bipartite graphs (Km,n)
K4,4
K3,3 is not planar.
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7/28/2019 Interaksi 3 Graph Theory
12/12Discrete Math by R.S. Chang, Dept. CSIE, NDHU 12
Hamilton Paths and Cycles
a path or cycle that contain every vertex
There is no known
necessary and sufficient condition for agraph to be Hamiltonian.
a b c
d e f
g h
i
There is a Hamilton path, but noHamilton cycle.