graphadjacency-matrixspanning-tree

Can a spanning tree contain a self loop?

I am referring to explanation of spanning tree given here.

I want to know can a spanning tree contain self loop? I.e. edge from one vertex to itself? I guess, no; because then for that loop there are two paths to reach that node. one direct and one including loop, but I want to confirm.

Solution

  • According to the Wikipedia article about trees, a tree is required to be cycle-free, which consequentially also holds for a spanning tree.