L(2, 1)-labeling of some special graphs
The L(2, 1)-labeling of a graph G is a mapping f : (V(G) → Z* such that | f(u) - f(v) | ≥ 2 if d(u, v) = 1 and | f(u) - f(v) | ≥1 if d(u,v) = 2. The L(2, 1)-labeling, number of G, denoted by λ(G), is the smallest number k such that G has an L(2, 1)-labeling with f(v) ≤ k for all v ϵ V(G). This paper...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
| Published: |
Animo Repository
2007
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/17473 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | The L(2, 1)-labeling of a graph G is a mapping f : (V(G) → Z* such that | f(u) - f(v) | ≥ 2 if d(u, v) = 1 and | f(u) - f(v) | ≥1 if d(u,v) = 2. The L(2, 1)-labeling, number of G, denoted by λ(G), is the smallest number k such that G has an L(2, 1)-labeling with f(v) ≤ k for all v ϵ V(G). This paper aims to present the L(2,1)-labeling and optimal L(2,1)-labeling of paths, cycles, wheels, complete graphs, trees, stars and hypercubes. All of the mentioned graphs are generalized except hypercube. The article entitled Labeling Graphs with a Condition at Distance 2, by Griggs and Yeh, served as the reference for this study. |
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