Graph Theory Basics - Questions
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The graph represents Euler's Konigsberg bridge problem.Â
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) 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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