Help! I'm Struggling with Graph Theory Exam!

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Discussion Overview

The discussion revolves around understanding the calculation of eigenvalues of adjacency matrices in graph theory, particularly in the context of an upcoming exam. Participants explore the implications of eigenvalues related to specific graph properties and seek resources for further clarification.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • The original poster expresses confusion about the connection between the sum of elements in a row of the adjacency matrix and the eigenvalues of graphs, specifically referencing the example of C_3.
  • One participant questions whether the graphs in question are undirected and if loops are allowed, noting that definitions can vary among authors.
  • Another participant confirms that the graphs are undirected and do not include loops.
  • A participant shares a link to a website that contains theorems related to eigenvalues, although its relevance to the original poster's specific issue is uncertain.

Areas of Agreement / Disagreement

Participants generally agree on the nature of the graphs being discussed (undirected without loops), but there is no consensus on the connection between eigenvalues and the sum of elements in the adjacency matrix, as the original poster remains confused.

Contextual Notes

The discussion does not resolve the original poster's confusion regarding the relationship between eigenvalues and the adjacency matrix, nor does it clarify the implications of the properties of the graphs being discussed.

Niels
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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 [itex]C_3[/itex] (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:
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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...
 

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