Strong Spanning Laceability of Mesh

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 , sk*L (G) , is the maximal value of G such that G is strong sk*L (G) -connected and sk*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  sk*L (M m,n) = 3  if mn is even and min {m,n} ≥ 4; otherwise sk*L (M m,n) ≤ 2.