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WorksheetsChapter 5 Network in Graph Theory
Total questions: 25
Worksheet time: 25mins
A simple graph has no loops. What other property must a simple graph have?
It must be directed.
It must be undirected.
It must have at least one vertex.
It must have no multiple edges.
Determine a simple graph.
All the graphs are simple graphs.
Which graph is a simple graph but not complete graph?
Which one is NOT a subgraph of the above graph?
The directed graph on the right shows the
roads connecting Lani’s house at A to the
school at E. Suggest the shortest route
that Lani can choose to cycle to school.
A > C > D > E
A > B > C > E
A > D > E
A > B > E
Determine the number of vertices and sum of degrees.
8,16
8,8
6,4
8,13
Determine the sum of degrees.
4
8
16
32
Determine n(E).
7
12
14
6
Determine n(V).
4
8
5
10
No arrows are shown on the edges.
Directed graph
Weighted graph
Simple graph
Undirected graph
An undirected and unweighted graph with no multiple edges.
Undirected graph
Unweighted graph
Incomplete graph
Simple graph
A loop is counted as _____ edge(s) but _____ degree(s).
one, two
one, one
two, two
two, one
State the number of vertices.
14
3.5
7
5
State Σd(V) .
5
7
10
14
State the number of edges.
18
7
9
6
Determine the sum of degrees.
16
8
4
13
Determine n(E).
7
12
14
6
If a tree has 10 edges, how many vertices does it have?
Jika satu pokok mempunyai 10 tepi, berapakah bucu yang terdapat dalam pokok tersebut?
11
10
9
8
E= { (P,Q) , (P,T) , (P,T) , (Q,T) , (Q,R) , (R,R) , (R,S) , (S,S) , (S,T) }
E= { (P,Q) , (P,T) , (,QT) , (Q,T) , (Q,R) , (R,R) , (R,S) , (R,S) , (S,T) }
E= { (P,Q) , (P,T) , (Q,T) , (Q,T) , (Q,R) , (R,R) , (R,S) , (S,S) , (S,T) }
E= { (P,Q) , (P,T) , (Q,T) , (Q,T) , (Q,R) , (R,S) , (R,S) , (S,S) , (S,T) }
din (1) = 2
din (3) = 2
dout (2) = 1
dout (3) = 1
Q⟶P⟶V⟶S
Q⟶S⟶P⟶V
Q⟶S⟶V⟶P
Q⟶V⟶P⟶S
Which of the following is TRUE about the edge of the graph shown above?
E = {(A, B), (B, C), (C, E), (E, F), (B, D), (D, E)}
E = {(A, B), (B, C), (C, E), (E, F), (D, B), (D, E)}
E = {(A, B), (B, C), (C, E), (E, F), (D, B), (E, D)}
E = {(F,E), (E,C), (D, E), (D, B), (B, A), (C, B)}
Choose ALL the CORRECT information for the simple graph given.
(Note: can choose more than one answers.)
V = {A, B, C, E, F, G}
V = {A, B, C, D, E, F, G}
E = {AB, AC, BC, BD, BE, CD, CF, DE, DF, EF, EG, FG}
n(E) = 12
What is the shortest path from A to D?
AED
ABFD
AECD
ABCFD
Calculate the shortest distance from v1 to v4 .
1000 m
1100 m
1400 m
2000 m
