Final answer:
Two nonisomorphic trees with the same degree sequence are a star tree with one center node connected to four leaves, and a binary tree with one root node, two children, each with one leaf. Both have a degree sequence of (4,1,1,1,1) but differ in structure.
Step-by-step explanation:
The student has asked to find two nonisomorphic trees with the same degree sequences. In graph theory, a tree is a connected undirected graph with no cycles. Two graphs are nonisomorphic if no graph isomorphism exists between them, meaning they cannot be made to look identical by simply renaming their vertices. The degree sequence of a tree is a list of the vertex degrees of its vertices. To answer the student's question, let's provide two examples:
- Tree 1: A star tree with 5 nodes - one center node connected to four leaves. The degree sequence is (4,1,1,1,1).
- Tree 2: A binary tree with 5 nodes - one root node, two children, and each child has one leaf. The degree sequence is also (4,1,1,1,1).
Both trees have the same degree sequence, but Tree 1 is star-shaped while Tree 2 is binary, and their structures are different, making them nonisomorphic.