Algebraic graph theory is the study of graphs using methods from algebra, particularly linear
algebra and group theory (Biggs 1993, Godsil
and Royle 2001).
Matrix methods use adjacency matrices and graph spectra to investigate the
structure of a graph. Group methods
use graph automorphism groups to study
vertex-transitive graphs and arc-transitive
graphs, and use Cayley graphs to construct graphs from groups. Polynomial
methods use objects such as the chromatic polynomial
to encode combinatorial information.
See also
Adjacency Matrix,
Algebraic Combinatorics,
Cayley Graph,
Chromatic
Polynomial,
Graph Automorphism Group,
Graph Spectrum,
Graph
Theory
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References
Biggs, N. L. Algebraic Graph Theory, 2nd ed. Cambridge, England: Cambridge University Press, 1993.
https://doi.org/10.1017/CBO9780511608704.Godsil,
C. and Royle, G. Algebraic
Graph Theory. New York: Springer-Verlag, 2001. https://doi.org/10.1007/978-1-4613-0163-9.
Cite this as:
Weisstein, Eric W. "Algebraic Graph Theory."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AlgebraicGraphTheory.html
Subject classifications
