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create a breadth first search tree centered at vertex 12 for the graph in figure 68 and use it to compute the distance
find a tree with more than one vertex that has the property that all the rooted trees you get by picking different
draw all rooted trees on 6 vertices with four leaf vertices if you would like to label the vertices as we did in the
draw all rooted trees on 5 vertices the order and the place in which you write the vertices down on the page is
a binary tree is a full binary tree if each vertex has either two nonempty children or two empty children a vertex with
a binary tree is a special kind of rooted tree that has some additional structure that makes it tremendously useful as
draw the minimum number of drawings of trees you can so that each tree with six vertices is represented by exactly one
find the strongest condition you can that has to be satisfied by a graph that has a path starting and ending at
try to find an interesting condition involving the degrees of the vertices of a simple graph that guarantees that the
suppose v 2k and consider a graph g consisting of two complete graphs one with k vertices x1xk and one with k 1
what is the minimum number of new bridges that would have to be built in kumlonigsberg and where could they be built in
if we built a new bridge in kumlonigsberg between the island and the top and bottom banks of the river could we take a
the hypercube graph qn has as its vertex set the n-tuples of zeros and ones two of these vertices are adjacent if and
we form the hamiltonian closure of a graph by constructing a sequence of graphs gi with g0 g and gi formed from gi-1
apply breadth-first search from vertex 0 in an alternating way to grapha in figure 626 does this method find an
table 62 shows a second sample of the kinds of applications a school district might get for its positions draw a graph
the k-path problem is the problem of determining whether a graph on n vertices has a path of length k where k is
the hamiltonian path problem is the problem of determining whether a graph has a hamiltonian path explain why this
a cut-vertex of a graph is a vertex whose removal along with all edges incident with it increases the number of
the complete bipartite graph kmn is a graph with m n vertices these vertices are divided into a set of size m and a
let g be a connected graph with no odd cycles let x beavertex of g let x be all vertices at an even distance from x and
what is the sum of the maximum size of an independent set and the minimum size of a vertex cover in a graph g hint it
consider the closed intervals 1 4 2 5 3 8 5 12 6 12 7 14 13 14 draw the interval graph determined by these intervals
a circuit is to be laid out on a computer chip in a single layer the design includes five terminals think of them as
as in the previous exercise we are laying out a computer circuit however we now have six terminals labeled a b c 1 2