The following question appeared in my examination :
Give an example to show that for a given graph G , spanning trees need not be unique .
but I was unable to construct an example for this ..
Can anyone kindly help me with this please ...
thanks in advance for any help.
Consider the complete graph $K_4$ on vertices $a,b,c,d$. Then the set of edges $ab,bc,cd$ is a spanning tree: a path of length $3$. But the set of edges $ab,ac,ad$ is another spanning tree, different (in the sense of not isomorphic) from the first since it has a vertex of degree $3$. Here is a picture, with the two trees in red: