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Consider the following graph. ei e2 es a e3 b e4 i (a) How many paths are there from a to c? (b) How many trails are there fr

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Answer #1

a) We know that a path between two vertices is a sequence of edges such that both the vertices and the edges in the sequence are distinct. Therefore, the number of paths from a to c in this graph is 4.

b) We know that a trail between two vertices is a sequence of edges such that only the edges are distinct. Therefore, the number of paths from a to c in this graph is = \binom41+\binom43 = 8 .

c) We know that a walk between two vertices is a sequence of edges. Therefore, since we can make infinite sequences of edges from a to c, the number of walks from a to c is infinite.

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