L3,2,1 labelling of kalpataru graph

Let G = (V, E) be a graph. An L(3,2,1) labelling 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 ∈ ℕ, a k − L(3,2,1) labelling is a labelling L(3,2,1) where all labels are not...

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Bibliographic Details
Main Authors: Sarbaini, Salman, A. N. M., Putra, G. L., Hamzah, M. L.
Format: Conference Proceeding
Language:English
Subjects:
Labelling
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Summary:Let G = (V, E) be a graph. An L(3,2,1) labelling 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 ∈ ℕ, a k − L(3,2,1) labelling is a labelling L(3,2,1) where all labels are not greater than k. An L(3,2,1) number of G, denoted by λ3,2,1(G), is the smallest non-negative integer k such that G has a k − L(3,2,1) labelling. In this paper, we determine λ3,2,1 of kalpataru graphs.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0181005