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

Abstract

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.