Help! I'm Struggling with Graph Theory Exam!

Click For Summary
Struggling with graph theory, the user seeks clarity on calculating eigenvalues of adjacency matrices, particularly in relation to a professor's question about the sum of elements in a specific row. They express confusion over their lecture notes and the connection between eigenvalues and the adjacency matrix. The discussion confirms that the graphs in question are undirected and do not allow loops. A resource from Berkeley is shared, containing theorems on eigenvalues that may assist in understanding. Overall, the user is looking for additional resources and clarification on these concepts.
Niels
Messages
10
Reaction score
0
I'm having an exam on graph theory next week and I'm having some problem with understanding the meaning of calculating eigenvalues of adjacency matrices for graphs. My notes suck from the lectures and I'm totally lost...

Our professor asked "What is the sum of elements in row k of the adjacency matrix?" and showed an example where he calculated the eigenvalues of C_3 (2, -1, -1) but then my notes stop and and I can't connect the eigenvalues to the question...

Any input on this subject most welcome... Any one know any good resource on the net where I can find more on this??
 
Last edited:
Mathematics news on Phys.org
I don't know of websites on that topic, though I don't doubt there are some.

Out of curiosity, in connection with your problem, are the graphs understood to be undirected? Can a node be adjacent to itself, i.e. are "loops" allowed in the type of graph you are talking about? I am pretty sure that different authors put different restrictions on the properties of a graph when defining that term.
 
The graphs are undirected without loops...
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Sudoku solver by graph coloring theory
  • · Replies 8 ·
Replies
8
Views
2K
Spectral Graph Clustering: where does the 'scoring' function come from
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What is the Cheapest Route to Visit 6 Destinations in Tokyo?
  • · Replies 17 ·
Replies
17
Views
2K
Evaluate the complexity of this graph coloring algorithm
  • · Replies 1 ·
Replies
1
Views
2K
Person i belongs to a clique iff ith diagonal entry of B^3 is positive
  • · Replies 9 ·
Replies
9
Views
2K
Help with Creating An Excel Line Graph
  • · Replies 1 ·
Replies
1
Views
1K
Adjacency matrices: (a) notation discrepancy, and (b) applications
  • · Replies 3 ·
Replies
3
Views
2K
MHB Understanding Two Graph Theory Problems
  • · Replies 2 ·
Replies
2
Views
2K
Finding the Magnetic Field (B_0) on a Graph [NMR]
  • · Replies 6 ·
Replies
6
Views
2K
Planning on studying math for the college entrance exam, help needed
  • · Replies 4 ·
Replies
4
Views
3K