Algebraic Graph Theory
Algebraic
graph theory
is a branch of
mathematics
. In one sense, algebraic graph theory studies
graphs
in connection with
linear algebra
. In particular it studies the
spectrum
of the
adjacency matrix
or
Laplace matrix
of a graph. This part of algebraic graph theory is also called the
spectral graph theory
. In the other sense, algebraic graph theory studies
graphs
in connection to
group theory
(particularly
geometric group theory
). In particular, the
automorphism group
of a graph plays an important role. The focus is placed on various families of symmetric graphs such as:
vertex-transitive graphs
,
edge-transitive graphs
,
arc-transitive graphs
,
Cayley graphs
, etc. *
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