Question

Proof a connected graph is unicursal if and only if it has exactly two vertices of odd degree

Answer 1

Answer:

Theorem 3.5 A connected graph is unicursal if and only if it has exactly two vertices of odd degree. Proof Let G be a connected graph and let G be unicursal. Then G has a unicursal line, say from u to v, where u and v are vertices of G. ... So every vertex of H is of even degree and thus H is Eulerian.