42)If x and y are nonadjacent vertices of T. then T+x, y, contains a simple circuit s There is a simple path from x to y in T. X-V:y s (x=Vi> Vils.,Vis v; y, Vi=x)o o 3)Next, we prove T+x, y) contains exactly a simple circuit o Suppose that there are two(or more than simple circuit in T+x, yj❖ 2) If x and y are nonadjacent vertices of T, then T+{x,y} contains a simple circuit ❖ There is a simple path from x to y in T. ❖ (x=vi ,vi1 ,…, vis,vj=y)。 ❖ (x=vi ,vi1 ,…, vis,vj=y,vi=x)。 ❖ 3)Next, we prove T+{x,y} contains exactly a simple circuit. ❖ Suppose that there are two (or more than) simple circuit in T+{x,y}