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Integer linear programming model and satisfiability test reduction for distance constrained labellings of graphs: the case of L(3,2,1)labelling for products of paths and cycles

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2 Author(s)
Zehui Shao ; Key Lab. of Pattern Recognition & Intell. Inf. Process., Instn. of Higher Educ. of Sichuan Province, China ; Vesel, A.

Let u and v be vertices of a graph G = (V, E) and d(u, v) be the distance between u and v in G. For positive integers k1, k2, ..., kn with $k_1 gt k_2 gt cdots gt k_n $k1>k2>⋯>kn an L(k1, k2, ..., kn)-labelling of G is a function f: V(G){0, 1, ...} such that for every u, v ∈ V(G) and for all 1 ≤ in, |f(u)- f(v)|ki if d(u, v) = i. The span of f is the difference between the largest and the smallest numbers in f(V(G)). The $lambda _{k_1 comma k_2 comma ldots comma k_n } $λk1,k2,...,kn-number of G is the minimum span over all L(k1, k2, ..., kn)-labellings of G. In this study, an integer linear programming model and a satisfiability test reduction for an L(k1, k2, ..., kn)-labelling are proposed. Both approaches are used for studying the λ3,2,1-numbers of strong, Cartesian and direct products of paths and cycles.

Published in:

Communications, IET  (Volume:7 ,  Issue: 8 )