Abstract
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.
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