Consider this adjacency matrix: 8 8 Draw the graph that this matrix represents What properties does this graph have? This adjacency matrix above is block diagonal and contains no self-loops. Suppose an adjacency matrix is block diagonal and does not contain self-loops. Will such matrix always represent graph with the property observed in the graph above? HINT Create 1-2 additional matrices that are block diagonal: Do these graphs also share this property? Suppose graph is disconnected. Will its adjacency matrix always have block diagonal property? Explain:
Added by Maureen M.
Close
Step 1
Draw the graph that this matrix represents: The adjacency matrix is given as: $$ \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} $$ This matrix represents a graph with two vertices connected by an edge. The graph can be drawn as: ``` 1 -- 2 ``` Show more…
Show all steps
Your feedback will help us improve your experience
Imogen Dell and 95 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Is every zero-one square matrix that is symmetric and has zeros on the diagonal the adjacency matrix of a simple graph?
Graphs
Representing Graphs and Graph Isomorphism
Describe the adjacency matrix of a graph with $n$ connected components when the vertices of the graph are listed so that vertices in each connected component are listed successively.
Connectivity
Are the simple graphs with the following adjacency matrices isomorphic? a) $\left[\begin{array}{lll}{0} & {0} & {1} \\ {0} & {0} & {1} \\ {1} & {1} & {0}\end{array}\right],\left[\begin{array}{lll}{0} & {1} & {1} \\ {1} & {0} & {0} \\ {1} & {0} & {0}\end{array}\right]$ b) $\left[\begin{array}{llll}{0} & {1} & {0} & {1} \\ {1} & {0} & {0} & {1} \\ {0} & {0} & {0} & {1} \\ {1} & {1} & {1} & {0}\end{array}\right],\left[\begin{array}{llll}{0} & {1} & {1} & {1} \\ {1} & {0} & {0} & {1} \\ {1} & {0} & {0} & {1} \\ {1} & {1} & {1} & {0}\end{array}\right]$ c) $\left[\begin{array}{llll}{0} & {1} & {1} & {0} \\ {1} & {0} & {0} & {1} \\ {1} & {0} & {0} & {1} \\ {0} & {1} & {1} & {0}\end{array}\right],\left[\begin{array}{llll}{0} & {1} & {0} & {1} \\ {1} & {0} & {0} & {0} \\ {0} & {0} & {0} & {1} \\ {1} & {0} & {1} & {0}\end{array}\right]$
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD
