Question

For each integer i with 1 ≤ i ≤ 4, give an example of a connected graph Gi of smallest order such that α(G) + α′(Gi) = 5 and α(Gi) = i.

Answer #1

give an example of a graph that is not weekly connected

(a) This exercise will give an example of a connected
space which is
not locally connected. In the plane R2
, let X0 = [0, 1] × {0},
Y0 = {0} × [0, 1], and for each n ∈ N, let Yn = {1/n} × [0,1]. Let
Y = X0 ∪ (S∞
n=0 Yn). as a subspace of R
2 with its usual topology.
Prove that Y is connected but not locally connected. (Note
that
this example also shows that...

Let n be a positive integer and G a simple graph of 4n vertices,
each with degree 2n. Show that G has an Euler circuit. (Hint: Show
that G is connected by assuming otherwise and look at a small
connected component to derive a contradiction.)

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.

Exercise 1.9.52. Give an example of a path connected space which is
not locally path connected

1) Give an example of a type I error.
2.
Give an example of a type II error.
3.
What type of t-test would you use when the same group is tested
twice at different time points?

Prove that if G is a connected graph with exactly 4 vertices of
odd degree, there exist two trails in G such that each edge is in
exactly one trail. Find a graph with 4 vertices of odd degree
that’s not connected for which this isn’t true.

Give an example of an application for using a series circuit
connected to a 6 V DC power source and another example of a
parallel circuit connected to a 12 V DC power source.

1) What is a Market Entrepreneur? What is a Political
Entrepreneur? Give an example of each in any other industry and
explain how they are different.
2) Give an example of an efficient monopoly and a coercive
monopoly and explain the positive or negative aspects of each.
3) In what ways did John D. Rockefeller make the world a better
place?
**Must be 4-5 sentences for each question.

What are the 4 types of market failure? Explain each and give an
example of each

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