smc-4788-20-Degrees of vertices

Networks, SMB-004

Find the number of vertices with an odd degree. (2 marks)

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`2`

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`text{Degrees of vertices (clockwise from top left):}`

`2, 3, 3, 2, 6`

`:.\ text{2 vertices have an odd degree.}`

Networks, SMB-002 MC

In the graph above, the number of vertices of odd degree is

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`C`

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`text{Two vertices have degree 3 (all others are even)}`

`=> C`

Networks, SMB-001 MC

The sum of the degrees of all the vertices in the graph above is

`6`
`9`
`11`
`12`

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`D`

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`text(Total Degrees)`	`=1+3+2+2+2+2`
	`=12`

`rArr D`

Networks, STD1 N1 2020 HSC 1 MC

Which of the following networks has more vertices than edges?

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`C`

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`text{Consider C:}`

`text{Graph has 5 vertices and 4 edges.}`

`=> \ C`

Networks, STD1 N1 2019 HSC 1 MC

A network diagram is given.

What is the degree of vertex `W`?

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`C`

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`text(Vertex)\ W\ text(has 3 edges connected and is therefore degree 3.)`

`=> C`

Networks, STD2 N2 2011 FUR1 1 MC

In the network shown, the number of vertices of even degree is

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`B`

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`text{Vertices with even degrees: 2, 2, 6}`

`=> B`

Networks, STD2 N2 2017 FUR1 2 MC

Two graphs, labelled Graph 1 and Graph 2, are shown below.

The sum of the degrees of the vertices of Graph 1 is

two less than the sum of the degrees of the vertices of Graph 2.
one less than the sum of the degrees of the vertices of Graph 2.
equal to the sum of the degrees of the vertices of Graph 2.
two more than the sum of the degrees of the vertices of Graph 2.

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`C`

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`text(Graph 1)`

`∑\ text(degrees)\ = 3 + 3 + 3 + 3 = 12`

`text(Graph 2)`

`∑\ text(degrees)\ = 2 + 2 + 2 + 2 + 2 + 2 = 12`

`=> C`