(a) Prove the following claim: in every simple graph G on at
least two vertices, we can always find two distinct vertices v,w
such that deg(v) = deg(w).
(b) Prove the following claim: if G is a simple connected graph
in which the degree of every vertex is even, then we can delete any
edge from G and it will still be connected.
Prove or disprove the following statements.
(a) There is a simple graph with 6 vertices with degree sequence
(3, 3, 5, 5, 5, 5)?
(b) There is a simple graph with 6 vertices with degree sequence
(2, 3, 3, 4, 5, 5)?
Please write step by step in details thanks will upvote
An entrepreneur opened a small hardware store in a street mall.
During the first few weeks, the business was slow with the store
averaging only one customer arrived every 20 minutes. Assume that
the random arrival of customers is Poisson distributed.
(a) What is the probability that exactly 5 customers arrive during
one-hour period?
(b) If the average revenue from each customer is USD 12, what is
the probability that...
Please attach the solution step by step, thanks!
1. An insurance company collected $31.0 million in premiums and
disbursed $28 million in losses. Loss adjustment expenses amounted
to $5.0 million. The firm is profitable
A. if dividends paid to policyholders is $4 million and income
generated on investments is $4 million.
B. if
dividends paid to policyholders is $10 million and income generated
on investments is $14 million.
C. if
dividends paid to policyholders is $6 million and income generated...
Please clear writing
and explain step by step this should be a simple
question
Consider the function
f : [0,1]→R defined by (f(x) =0 if x = 0) and (f(x)=1 if 0
< x≤1)
(i)Compute L(f)
andU(f).
(ii) Is f Riemann
integrable on [0,1]?
Prove or disprove: If G = (V; E) is an undirected graph where
every vertex has degree at least 4 and u is in V , then there are
at least 64 distinct paths in G that start at u.