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 $v _ { 2 }$ ?

---

Definitions:

Mission Statement

A concise description of an organization's purpose, identifying its scope of operations, and guiding its decision-making.

Profit

The financial gain that results when the amount of revenue gained from a business activity exceeds the expenses, costs, and taxes needed to sustain the activity.

Marketing Plan

A comprehensive document or blueprint outlining a business's advertising and marketing efforts for the coming period.

Mission

A statement or vision that defines the fundamental purpose of an organization, guiding its operations and goals.