Final answer:
Every edge of a tree is a cut-edge. A tree with 30 vertices has 29 edges. In a 5-ary tree of height 6, there are at most 15625 leaves.
Step-by-step explanation:
(a) Every edge of a tree is or is not a cut-edge?
In a tree, every edge is a cut-edge. This means that if an edge is removed, it will disconnect the tree into two separate components.
(b) A tree with 30 vertices has how many edges?
A tree with n vertices has exactly n-1 edges. Therefore, a tree with 30 vertices will have 30-1 = 29 edges.
(c) In a 5-ary tree of height 6, there are at most how many leaves?
In a 5-ary tree, each node can have at most 5 children. The number of leaves in a 5-ary tree of height 6 can be calculated as 5^6, which is equal to 15625.
(d) Is the graph of 3 a tree? Explain why or why not.
No, the graph of 3 is not a tree. A tree must have n-1 edges for n vertices. The graph of 3 has 2 edges, violating this condition.
(e) How many leaves does a 5-ary tree have if it has 20 parents & every parent has exactly 3 children?
In this case, each parent has 3 children. Therefore, the number of leaves can be calculated as 20 * 3 = 60.