The 1-skeleton is the 
case of the p-skeleton of a simplicial
complex or CW-complex. For a simplicial
complex 
,
it is the simplicial subcomplex 
consisting of its vertices
and edges. For a CW-complex 
, it is the union 
of the zero- and one-dimensional cells (Hatcher 2002).
For a map represented by a cellular embedding of a graph in a surface, the 1-skeleton is the embedded graph formed by the vertices and edges. Its underlying graph is obtained by forgetting the interiors of the faces and the supporting surface (Gross and Tucker 1987).
