# Draw a graph that has [ 0 0 0 1 2 0 0 0 1 1 0 0 0 2 1 1 1 2 0 0 2 1 1 0 0 ] as its adjacency matrix. Is this graph biparitite? Definition: Given an m × n matrix A whose ijth entry is denoted a i j , the transpose of A is the matrix A’ whose ijth entry is a i j , for each i = 1 , 2 , … , m and j = 1 , 2 , … , n . Note that the first row of A becomes the first column of A t , the second row of A becomes the second column of A t , and so forth. For instance. if A = [ 0 2 1 1 2 3 ] , then A t = [ 0 1 2 2 1 3 ] . b. Show that a graph with ii vertices is bipartite if, and only if , for some labeling of its vertices, its adjacency matrix has the form [ O A A t O ] where A is a k × ( n − k ) matrix for some integer k such that 0 &lt; k &lt; n , the top left O represents a k × k matrix all of whose entries are 0, A t is the transpose of A, and the bottom right O represents an ( n − k ) × ( n − k ) matrix all of whose entries are 0.

### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

#### Solutions

Chapter
Section
Chapter 10.2, Problem 22ES
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