Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Functional programming, design and analysis of algorithms (resit) / 8 / b / ii

True. Every finite tree on $|V|$ vertices has exactly $|V|-1$ edges. One proof removes a leaf and its incident edge, preserving a tree on one fewer vertex, and applies induction from the one-vertex tree. Therefore all minimum spanning trees have the same edge count.