A total labeling of a graph G is an assignment of integers 1,2, ..., |V (G)| + |E(G)| to vertices and edges of G. In this paper, we present two results on the total labeling of the grid Pm□P_n (m,n ≥ 2). The first result is about magic total labeling (a notion involving constant sum). We prove that P_m□P_n, (m, n ≥ 2) is C4-supermagic. This settles an open problem proposed by Ngurah, Salman and Susilowati in [H-supermagic labelings 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□P_n (m, n ≥ 2) is (2mn + 2, 1)-super-edge-antimagic total.
展开▼
