Question

Please explain what Euler Trail for this is and Hamilton Cycle, and how to draw the shape / solve the entire/ full question.

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B9. Consider the following graph G: (a) Either give an euler trail in G or prove that no such trail exists. (b) Either give a hamilton cycle in G or prove that no such cycle exists. (c) Calculate (G)- the number of spanning trees of G. Show your work.

Answer 1

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V V3 solution First, let us label the Go vertices as {1, 2, 3, 4,5} as. (a) for a graph to have a Euler trail, a Graph must be Eulerian. And A graph is Eulerian if and only if degree of all vertices is even. Now since in graph G , there are 4 vertices with odd degree, namely {2, 3, 4, 5} → No Euler trail ex , (6) Yes, there exists a hamiltonian cycle & èt is 12-23-35-54-41.