What is the value of v eat the end of the pruning process w

What is the value of v - eat the end of the pruning process, when the tree has been reduced down to a single vertex? What does that mean about the original value of v - e?

Solution

We know in Pruning process of any tree, we always end up with only one vertex and no edges.

that means v=1 and e=0

v-e=1-0=1

that means value of v-e at the end of pruning process is always 1.

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Now second part of questin

By Tree theorem we know that \"Every tree with v vertices has exactly v-1 edges\"

that means if v=v then e=v-1

Hence v-e=v-(v-1)=v-v+1=1

so original value of v-e=1

we also got v-e=1 from first part.

That means value of v-e remans always 1 at each step of Pruning process of tree.