Suppose that a connected graph without loops or parallel edges
has 11 vertices, each of degree...
Suppose that a connected graph without loops or parallel edges
has 11 vertices, each of degree 6. a. Must the graph have an Euler
Circuit? Explain b. Must the graph have a Hamilton Circuit? Explain
c. If the graph does have an Euler Circuit, how many edges does the
circuit contain? d. If the graph does have a Hamilton Circuit, what
is its length?
How many trees T are there on the set of vertices
{1, 2, 3, 4, 5,...
How many trees T are there on the set of vertices
{1, 2, 3, 4, 5, 6, 7} in which the vertices 2 and 3 have degree 3,
vertex
5 has degree 2, and hence all others have degree 1? Do not
just
draw pictures but consider the possible Pr¨ufer codes of these
trees.
A spanning tree of connected graph G = (V, E) is an acyclic
connected subgraph (V,...
A spanning tree of connected graph G = (V, E) is an acyclic
connected subgraph (V, E0 ) with the same vertices as G. Show that
every connected graph G = (V, E) contains a spanning tree. (It is
the connected subgraph (V, E0 ) with the smallest number of
edges.)
Give an example of a connected undirected graph that contains at
least twelve vertices that contains...
Give an example of a connected undirected graph that contains at
least twelve vertices that contains at least two circuits. Draw
that graph labeling the vertices with letters of the alphabet.
Determine one spanning tree of that graph and draw it. Determine
whether the graph has an Euler circuit. If so, specify the circuit
by enumerating the vertices involved. Determine whether the graph
has an Hamiltonian circuit. If so, specify the circuit by
enumerating the vertices involved.
10.-Construct a connected bipartite graph that is not a tree
with vertices Q,R,S,T,U,V,W.
What is the...
10.-Construct a connected bipartite graph that is not a tree
with vertices Q,R,S,T,U,V,W.
What is the edge set?
Construct a bipartite graph with vertices Q,R,S,T,U,V,W such
that the degree of S is 4.
What is the edge set?
12.-Construct a simple graph with vertices F,G,H,I,J that has an
Euler trail, the degree of F is 1 and the degree of G is 3.
What is the edge set?
13.-Construct a simple graph with vertices L,M,N,O,P,Q that has
an Euler circuit...