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D1 graph theory

The question asks "A simple graph G has 5 vertices and each has the same degree d. State the possible values of d"

The answer is 0,1,2,3,4 but how can it be 1? I must be missing something really obvious that will have me kicking myself when you show me.

Thanks
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Avatar for RhyaCeri
RhyaCeri
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Simple graphs don't have to all be connected


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Original post by RhyaCeri
Simple graphs don't have to all be connected


Posted from TSR Mobile


That doesn't answer the question though, if the graph has an odd number of vertices, then how can the order of each of them be 1?
Original post by RhyaCeri
Simple graphs don't have to all be connected


Posted from TSR Mobile


Yes but if there are 5 vertices and each has a degree of one, what does it look like? As far as I can see you can join 2 vertices and a different 2 vertices giving each a degree of one but the other vertex can't join to anything. I'm stuck.
It can only be 1 if the number of vertices is even, so it's impossible for a graph with 5 vertices to each have a degree of 1
Original post by MisterLuke96
It can only be 1 if the number of vertices is even, so it's impossible for a graph with 5 vertices to each have a degree of 1


Thank you. (The question is in Advancing Maths for AQA Decision Maths 1. )

Is there any way of working out the answer to questions like that without trying to draw the graphs?
How do you work these questions out?
I think it's easier just to draw the graphs out.


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