The L(2,1)-Labeling of Planar Graphs with Neither 3-Cycles Nor Intersect 4-Cycles

Given a graph G, a k-L(2,1)-labelling of G is a function c: V(G)→{0,1,2,…,k} such that | ϕ ( x )- ϕ ( y )| ≥ 2 if x is adjacent to y and | ϕ ( x )- ϕ ( y )| ≥ 1 if x and y have a common neighbor. The least k denoted by λ 2,1 (G) is the L(2, 1)-labelling number. In this article, we proved that: for every planar graph with neither 3-cycles nor intersect 4-cycles and Δ( G ) ≥ 26, λ 2,1 ( G ) ≤ Δ( G ) + 12.