   Chapter 10.2, Problem 6ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# The following are adjacency matrices for graphs. In each case determine whether the graph in connected by analyzing the matrix without drawing the graph. [ 0 1 1 1 1 0 1 0 0 ] [ 0 2 0 0 2 0 0 0 0 0 1 1 0 0 1 1 ]

To determine

(a)

Whether the graph is connected by analyzing the matrix without drawing the graph.

Explanation

Given information:



Calculation:

The adjacency matrix A = [aij] is n×n zero-one matrix with

aij={1                     if there is an edge from  v i to  v j0                    otherwise

A graph is connected if there exists a walk between every pair of vertices.



The given adjacency matrix is a 3x3-matrix, which implies that the corresponding graph contains 3 vertices

To determine

(b)

Whether the graph is connected by analysing the matrix without drawing the graph..

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