Discuss the below:
Q1: Let u and v be arbitrary vertices of a connected graph G. Show that there exists a u-v walk containing all vertices of G
Q2: Prove that a graph G is connected if and only if for every partition V(G) = Vi U 14, there exists an edge of G joining a vertex of VI and a vertex of V2.
Q3: Prove that if G is a graph with 8(G) > 2, then G contains a cycle.
Q4: Prove that every graph G has a path of length 8(G).