Consider the tree given below: Using the property of eccentricity of a vertex,…
2012
Consider the tree given below:
Using the property of eccentricity of a vertex, find every vertex that is the center of the given tree:
- A.
d & h
- B.
c & k
- C.
g, b, c, h, j, m
- D.
c & h
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Correct answer: D
First, determine the diameter of the tree by finding the longest path between any two vertices. Here, the longest paths have length 5 (e.g., a to j). The center consists of vertices with minimum eccentricity, which is ceil(diameter/2) = 3. Vertex c has a maximum distance of 3 to vertex j, and vertex h has a maximum distance of 3 to vertex a. Since both have the minimum eccentricity, they are the centers.
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