Interaksi 3 Graph Theory

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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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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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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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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degree/order of a vertex

is the number of edges

Incident on it


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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


7/12Discrete Math by R.S. Chang, Dept. CSIE, NDHU 7


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



a

b

d

e

disconnected withtwo components

a

b

c

d

e

Connected graph


c



A complete graph is a simple graph in

which every pair of vertices isconnected by an edge

a

b

c

d

e

K5




Planar Graphs

A graph (or multigraph) G is calledplanarifG can bedrawn in the plane with its edges intersecting only at vertices ofG.

K4 K5



Planar Graphs

Bipartite graph and complete bipartite graphs (Km,n)

K4,4

K3,3 is not planar.



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.

Interaksi 3 Graph Theory

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