L(3,2,1) Labeling of Firecracker Graph

Sarbaini Sarbaini (Universitas Islam Negeri Sultan Syarif Kasim)
Salman A.N.M. (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung)
Ganesha Lapenangga Putra (Department of Mathematics, Faculty of Sciences and Technology, Universitas Nusa Cendana)

Journal of the Indonesian Mathematical Society
VOLUME 29 NUMBER 1 (MARCH 2023)

Let G = (V, E) be a graph. An L(3,2,1) labeling of G is a function f : V → N ∪ {0} such that for every u, v ∈ V , |f(u) − f(v)| ≥ 3 if d(u, v) = 1, |f(u) − f(v)| ≥ 2 if d(u, v) = 2, and |f(u) − f(v)| ≥ 1 if d(u, v) = 3. Let k ∈ N, a k − L(3, 2, 1) labeling is a labeling L(3,2,1) where all labels are not greater than k. An L(3,2,1) number of G, denoted by λ(3,2,1)(G), is the smallest non-negative integer k such that G has a k − L(3,2,1) labeling. In this paper, we determine λ(3,2,1) of firecracker graphs.