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WorksheetsChapter 5: Network in Graph Theory (F4)
Total questions: 20
Worksheet time: 15mins
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?
By looking at the pattern of the numbers in the table, determine the number of edges for a complete graph to be drawn from 9 nodes given.
28
36
45
55
Which one is NOT a subgraph of the above graph?
Which of the following statements in not true?
V={ P, Q, R, S, T, U}
E= {(P,P), (P,R), (R,S), (S,T), (T,S), (R,Q), (Q,P)}
d(P) = 3
sum of degree = 14
Which of the statements below is not true
V = {P, Q, R, S, T, U}
E = {(R,S), (S,T), (T,U), (U,P), (P,Q)}
d(R) = 3
sum of degree = 18
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
Find Σd(v).
5
10
12
24
Determine the sum of degrees.
4
8
16
32
Determine n(E).
7
12
14
6
Determine n(V).
4
8
5
10
Choose the correct term to match each definition: Lines or curves that connect vertices.
Regions
Vertices
Edges
Paths
An edge that begins and ends at the same vertex.
Multiple edges
Vertices
Loop
Node
Links that connect the same two vertices to one another.
Multiple edges
Vertices
Loop
Nodes
When the edges have a numerical representation (to indicate length, time, capacity etc.).
Multiple edges
Weighted graph
Complete graph
Directed graph
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
