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Graph TheoryEasyEulerian and Hamiltonian Graphs

Eulerian and Hamiltonian Graphs · Easy problem

A graph GG has vertices 1,…,61,\ldots,6: a triangle on 1,2,31,2,3 (edges 12,23,3112,23,31), a separate triangle on 4,5,64,5,6 (edges 45,56,6445,56,64), and one edge 3636 joining the two triangles. GG has an Euler trail but no Euler circuit. Find the product of the two vertices between which that trail must run.