Consider the Adjacency Matrix for a Graph That Is Shown $v _ { 1 }$

question 8

Essay

Consider the adjacency matrix for a graph that is shown below. Answer the following questions by examining the matrix and its powers only, not by drawing the graph. Show your work in a way that makes your reasoning clear.
(a) How many walks of length 2 are there from $v _ { 1 }$ to $v _ { 2 }$ ?
(b) How many walks of length 2 are there from $v _ { 1 }$ to $v _ { 3 }$ ?
(c) How many walks of length 2 are there from $v _ { 2 }$ to $v _ { 2 }$ ?

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Definitions:

Employees' Expectations

Employees' expectations encompass the assumptions and desires employees have regarding their work environment, responsibilities, benefits, and how they wish to be treated by their employers.

One-To-One Relationship

A direct and unique connection or correspondence between two entities in a context, such as database elements or personal interactions.

Effective Managers

Individuals who successfully achieve organizational goals through planning, leading, organizing, and controlling resources.

Human Resources

The department of a business or organization that deals with the hiring, administration, and training of personnel.