A graph consists of vertices and edges. And vertices
are connected to each other by edges. From this point
of view, graphs can be identiﬁed with
1dimensional
CWcomplexes
. As topological objects, graphs don’t look
illuminating. Graphs are, however, useful when we
describe combinatorial data mathematically. As a
generalization of
knot theory
, we can study embeddings of graphs topologically.
Ribbon graphs
are also important in lowdimensional topology.
There are many variations. We can color vertices or
edges. We can also orient edges. Directed graphs are
called
quivers
.
