**Ahmad Zainy Al-Yasry ^{[1]}**

[1] : University of Baghdad, College of Science for Women, Department of Mathematics, Baghdad, IRAQ

**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.

**References**

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[MR2174270]

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[3] L. H. Kauffman, *Invariants of graphs in three-space*,
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[MR2173845]

[6] P. Turner, *Five lectures on Khovanov homology*, arXiv:math/0606464 [math.GT] (2006).

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