Suppose You Have a Graph G with Vertices V₁, V₂ $v _ { 5 } \text { to } v _ { 3 }$

question 21

Essay

Suppose you have a graph G with vertices v₁, v₂, . . . , v₁₇. Explain how you would use the adjacency matrix A to find
(a) The number of paths from $v _ { 5 } \text { to } v _ { 3 }$ of length 12.
(b) The length of a shortest path from $v _ { 5 } \text { to } v _ { 3 }$ .

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Definitions:

Purchase Option

A clause in a contract that allows one party to purchase goods or assets from the other party at a predetermined price within a specified timeframe.

Market Rate of Interest

The prevailing rate at which interest is paid by borrowers for loans or earned by investors in the financial markets.

Face Value

The nominal or original value stated on a security or financial instrument, such as a bond or stock, at the time of its issue.

Interest Rate

The proportion of a loan that is charged as interest to the borrower, typically expressed as an annual percentage of the loan amount.