(a) Show that a graph G with at least three vertices is 2-connected if and only if any vertex and any edge of G lie on a common cycle of G: (b) Show that a graph G with at least three vertices is...

(a) Show that a graph G with at least three vertices is 2-connected if and only if any vertex and any edge of G lie on a common cycle of G:

(b) Show that a graph G with at least three vertices is 2-connected if and only if any two edges of G lie on a common cycle