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Year 11 Maths - General Graphs and Networks

Graph Theory Basics

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Questions
Question 1
31159

The graph represents Euler's Konigsberg bridge problem. 

i) How many edges are there?
ii) How many vertices are there?
iii) How many vertices with an even degree are there?
iv) How many vertices with an odd degree are there?

i) 7  ii) 4 iii) 0  iv) 4

i) There are a total of 7 edges.
    Minor arc \(AB\)         Lines: \(AD, BD\) and \(CD\)
    Major arc \(AB\)
    Minor arc \(BC\)
    Major arc \(BC\)

ii) There are 4 vertices
    The points labelled \(A, B, C\) and \(D\).


iii) The degrees are:
     \(A \rightarrow 3, B \rightarrow 5, C \rightarrow 3 \text { and } D \rightarrow 3\)
     \(\therefore\) There are 0 vertices with even degrees

iv) The degrees are:
     \(A \rightarrow 3, B \rightarrow 5, C \rightarrow 3 \text { and } D \rightarrow 3\)
     \(\therefore\) There are 4 vertices with odd degrees

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