For any n ≥ 1 let Kn,n be the complete bipartite graph (V, E)
where V = {xi : 1 ≤ i ≤ n} ∪ {yi : 1 ≤ i ≤ n} E = {{xi , yj} : 1 ≤
i ≤ n, 1 ≤ j ≤ n} (a) Prove that Kn,n is connected for all n ≤ 1.
(b) For any n ≥ 3 find two subsets of edges E 0 ⊆ E and E 00 ⊆ E
such...
Write down the chromatic polynomials of
(i)the complete graph K7;
(ii)the complete bipartite graph K1,6.
In how many ways can these graphs be coloured with ten colours?
is the graph showing normal
distribution. explain
Tme of the day
Aggregation
values
Day-time (n = 16)
6.23
6.91
6.35
6.29
6.45
6.30
6.60
6.54
6.64
6.90
6.11
7.28
6.93
7.89
7.21
6.90
Night-time (n = 16)
6.41
5.98
6.25
6.03
6.57
6.25
6.51
6.50
6.50
6.41
6.70
6.03
6.60
6.77
6.88
6.93
Data analysis.
Summarize the data.
find hypothesis test
is the above graph shows normal
distribution or not. explain n detail
Question 2: A bipartite graph with 2n vertices (namely |V1| =
|V2| = n) is d-regular if and only if the degree of every vertex in
V1 ∪ V2 is exactly d. Show that a d-regular bipartite graph always
has a perfect matching (a matching of size n that includes all
vertices).
***Remarks: All the graphs here are without self loops and
parallel or anti-parallel edges. A network is a directed graph with
source s and sink t and capacity...
(Please attach a graph showing your work for question 2)
Suppose that the coronavirus pandemic (COVID 19) in 2020 has
resulted in a leftward shift of the aggregate demand curve (it has
also shifted the short-run aggregate supply to the left, but let’s
ignore this effect here for simplification).
A. Use the aggregate-demand/aggregate-supply model to show the
effects on output and the price level/inflation in both the short
run and long run (assume that the short-run aggregate supply curve
is...
Consider the m by n grid graph: n vertices in each of m rows,
and m vertices in each of n columns arranged as a grid, and edges
between neighboring vertices on rows and columns (excluding the
wrap-around edges in the toric mesh). There are m n vertices in
total.
a)What is the diameter of this graph?
b) From the top left vertex to the bottom right vertex, how many
shortest paths are there? Please explain.
1.
Agile Methods Practice Problems. Complete these problems, showing
your work.
1a. At the end of Day 1 of a
sprint there are 90 story points worth of work remaining, and at
the end of Day 6 there are 40 story points of work remaining. What
is the project’s current velocity, in units of story points per
day? (Show your work)
1b. A project whose sprint
velocity is 12 story points per day at the end of Day 4, and...
Showing your work and including the appropriate diagrams where
they should be obvious to include, determine the following and
highlight your final answer:
a) The value of zα/2 when determine the 96% confidence interval
for p.
b) The decision rule (aka, the rejection region) for testing the
following pair of hypotheses at the .05 level of significance when
the population standard deviation is unknown and a random sample of
size 28 is taken. H0: µ = 18 Ha: µ <...