A graph G is said to have a totally magic cordial labeling with constant C if there exists a mapping f : V(G) U E(G) → {0,1} such that f (a) + f (b) + f (ab) ≡ C (mod 2) for all ab ∈ E(G) and |nf (0) — nf (1)| ≤ 1, where nf(i) (i = 0, 1) is the sum ofthe number ofvertices and edges with label i. In this paper we establish that mPn and mKn are totally magic cordial for various values of m and n.