A cycle-magic labeling and an edge-antimagic labeling of the grid

A total labeling of a graph G is an assignment of integers 1, 2,..., vertical bar V(C)vertical bar + vertical bar E(G)vertical bar to vertices and edges of G. In this paper, we present two results on the total labeling of the grid P-m square P-n (m,n >= 2). The first result is about magic total labeling (a notion involving constant sum). We prove that P-m square P-n (m, n >= 2) is C-4-superrnagic. This settles an open problem proposed by Ngurah, Salman and Susilowati in [H-supermagic labelinys of graphs, Discrete Math. 310(2010)]. The second result is about antimagic total labeling (a notion involving distinct sums). We prove that the P-m square P-n (m,n >= 2) is (2mn + 2, 1)-super-edge-antimagic total.