Strong Spanning Laceability of Mesh

A bipartite graph G is strong k^*-laceability if there is a r^*-container between any two distinct nodes x and y form different partite sets of G with r ≤ min{deg(x),deg(y),k}. The strong spanning laceability of G , sκ_L^*(G), is the maximal value of G such that G is strong sκ_L^*(G)-connected and sκ_L^*(G) ≤ Δ(G) where Δ(G) is the maximal degree of G . Let M_m,n be the mesh with m rows and n columns. In this paper, we show that sκ_L^*(M_m,n)=3 if mn is even and min{m,n}≥ 4; otherwise sκ_L^*(M_m,n)≤2.