4. For each of the following requirement, please give a proper representation of graph G (V, E) in Fig 1.
(a) Find all vertices that are adjacent to a specified vertex Vi in time proportional to the
number of vertices reported. (5%)
(b) Determine whether two specified vertices V; and V; are adjacent in constant time.
(5%)
(c) How many paths whose length is 8 from node V, to node Vs exists in the graph ?
(10%)

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

b and c

step-by-step explanation:

should have been evaluated with one odd value and one even value. the expressions have equivalent values when . when , the first expression has a value of 3 and the second

step-by-step explanation: