Graph eigenvalues are typically denoted and ordered with . The largest eigenvalue
absolute value in a graph is called the spectral radius
of the graph, and the second smallest eigenvalue of the Laplacian
matrix of a graph is called its algebraic
connectivity. The sum of absolute values of graph eigenvalues is called the graph energy.
The notation
is also used for graph eigenvalues (e.g., Godsil and Royle 2001, p. 193), though
sometimes with an indexing convention starting with being the smallest (instead of ). A graph with graph
diameter
has a graph spectrum consisting of at least distinct eigenvalues, with the bound
becoming tight for a distance-regular graph,
which has exactly
distinct eigenvalues (Fallat et al. 2024).
For a strongly regular graph with parameters that is not a complete
or empty graph, there are exactly three graph eigenvalues
, , and with and , where are the roots of
and ordered with 
. The largest eigenvalue
absolute value in a graph is called the spectral radius
of the graph, and the second smallest eigenvalue of the Laplacian
matrix of a graph is called its algebraic
connectivity. The sum of absolute values of graph eigenvalues is called the graph energy.
is also used for graph eigenvalues (e.g., Godsil and Royle 2001, p. 193), though
sometimes with an indexing convention starting with 
being the smallest (instead of 
). A graph with graph
diameter 
has a graph spectrum consisting of at least 
distinct eigenvalues, with the bound
becoming tight for a distance-regular graph,
which has exactly 
distinct eigenvalues (Fallat et al. 2024).
that is not a complete
or empty graph, there are exactly three graph eigenvalues
, 
, and 
with 
and 
, where 
are the roots of
