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...
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?
Consider the complete bipartite graph Kn,n with 2n vertices. Let
kn be the number of edges...
Consider the complete bipartite graph Kn,n with 2n vertices. Let
kn be the number of edges in Kn,n. Draw K1,1, K2,2 and K3,3 and
determine k1, k2, k3. Give a recurrence relation for kn and solve
it using an initial value.
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.
Find the diameters of Kn (Connected graph with n vertices), Km,n
(Bipartite graph with m and...
Find the diameters of Kn (Connected graph with n vertices), Km,n
(Bipartite graph with m and n vertices), and Cn (Cycle graph with n
vertices). For each, clearly explain your reasoning.