  This paper is devoted to qualgebras and squandles, which are quandles
enriched with a compatible binary/unary operation. Algebraically, they are
modeled after groups with conjugation and multiplication/squaring operations.
Topologically, qualgebras emerge as an algebraic counterpart of knotted
3-valent graphs, just like quandles can be seen as an "algebraization" of
knots; squandles in turn simplify the qualgebra algebraization of graphs.
Knotted 3-valent graph invariants are constructed by counting
qualgebra/squandle colorings of graph diagrams, and are further enhanced using
qualgebra/squandle 2-cocycles. Some algebraic properties and the beginning of a
cohomology theory are given for both structures. A classification of size 4
qualgebras/squandles is presented, and their second cohomology groups are
completely described.
