I got confused about minimal and minimum in context of graph theory. Although, I have understanding that minimal means more than one minimum i.e. none qualifies as actual minimum so we say them minimal.
What exactly does minimal spanning tree mean? Also, what exactly does 'minimal edge' mean?
How do they differ from minimum spanning tree? How are 'minimal edge' different from minimum edge?
This doubt arose due to the statement:
S: There exists a minimum weight edge in G, which exists in every minimum spanning tree of G.
Can we say on using word 'minimum' it's implied that there is only one minimum weight edge. Besides, statement used "exists" which is singular.