  A discussion given to the question of extending Khovanov homology from links
to embedded graphs, by using the Kauffman topological invariant of embedded
graphs by associating family of links and knots to a such graph by using some
local replacements at each vertex in the graph.
  This new concept of Khovanov-Kauffman homology of an embedded graph
constructed to be the sum of the Khovanov homologies of all the links and knots
associated to this graph.
