Consider the network diagram - HSC - SSCE Mathematics Standard - Question 2 - 2021 - Paper 1
Question 2
Consider the network diagram.
What is the sum of the degrees of all the vertices in this network?
A. 5
B. 8
C. 14
D. 16
Worked Solution & Example Answer:Consider the network diagram - HSC - SSCE Mathematics Standard - Question 2 - 2021 - Paper 1
Step 1
Identify the Vertices and Edges
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Answer
In the given network diagram, we have the following vertices: A, B, C, D, E. The edges connecting these vertices are AB, BC, CD, and AE. Counting these gives us a total of 4 edges.
Step 2
Calculate the Degree of Each Vertex
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Answer
The degree of a vertex is the number of edges incident to it.
Vertex A: 2 edges (AB and AE)
Vertex B: 2 edges (AB and BC)
Vertex C: 2 edges (BC and CD)
Vertex D: 1 edge (CD)
Vertex E: 1 edge (AE)
Step 3
Sum the Degrees
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Answer
To find the sum of degrees of all vertices, we calculate:
Degree of A + Degree of B + Degree of C + Degree of D + Degree of E = 2 + 2 + 2 + 1 + 1 = 8.
Step 4
Determine the Final Answer
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Answer
The sum of the degrees of all the vertices in this network is 8. Therefore, the answer is B. 8.
