Chapter 11: Q5E (page 755)
Is the rooted tree in Exercise \(3\) a full \({\bf{m}}\)-ary tree for some positive integer \({\bf{m}}\)?
Rooted tree is not a m-ary tree
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The eccentricity of a vertex in an unrooted tree is the length of the longest simple path beginning at this vertex. A vertex is called a center if no vertex in the tree has smaller eccentricity than this vertex. In Exercises \({\bf{39--41}}\) find every vertex that is a center in the given tree.
41.
Find the second least expensive communications network connecting the five computer centers in the problem posed at the beginning of the section.
a) How many edges does a tree with \({\bf{n}}\) vertices have?
b) What do you need to know to determine the number of edges in a forest with \({\bf{n}}\) vertices?
In Exercises 2–6 find a spanning tree for the graph shown byremoving edges in simple circuits.
Explain how breadth-first search and how depth-first search can be used to determine whether a graph is bipartite.
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