L(2, 1)-labeling of some special graphs

• Main Authors: Juan, Jeremiah P., Padilla, Jezreel I.
• Format: text
• Language: English
• Published: Animo Repository 2007
• Subjects: Graph theory
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/17473
• Institution: De La Salle University

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.