A graph theory terminology challenge


Suppose we take the complete bipartite graph K_{m,n}, choose one of the
two partite sets, and then add an edge between every pair of vertices
belonging to this partite set. What is this type of structure usually
called? Is there any standard notation used to represent it?

(To be clear: if the partite sets are A and B, with |A| = m and |B| =
n, and we choose to add the extra edges to A, then the final graph
would have (m(m-1)/2) + mn edges altogether - namely, all m(m-1)/2
possible edges within A, along with all mn possible edges between A and
B.)

Cheers in advance,

TP

.

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