Draw a graph that has
as its adjacency matrix. Is this graph biparitite?
Definition: Given an matrix A whose ijth entry is denoted , the transpose of A is the matrix A’ whose ijth entry is , for each and .
Note that the first row of A becomes the first column of , the second row of A becomes the second column of , and so forth. For instance.
if , then .
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 where A is a matrix for some integer k such that , the top left O represents a matrix all of whose entries are 0, is the transpose of A, and the bottom right O represents an matrix all of whose entries are 0.
Draw a graph that has as its adjacency matrix. Is this graph bipartite?
A bipartite graph is a simple graph whose vertices can be partitioned into two sets V1 and V2 such that there are no edges among the vertices of V1 and no edges among the vertices of V2, while there can be edges between a vertex of V1 and vertex V2.
The give adjacency matrix is a -matrix, which implies that the corresponding graph contains 5 vertices. Let us name these vertices
Show that a graph with n vertices is bipartite if, and only if, for some labelling of its vertices, its adjacency matrix has the form .
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started