No-hole $\lambda$-$L(k, k-1, \ldots, 2, 1)$-labeling for Square Grid

Abstract

Given a fixed k ∈ Z and λ ∈ Z, the objective of a λ-L(k, k − 1, . . . , 2, 1)-labeling of a graph G is to assign nonnegative integers (known as labels) from the set {0, . . . , λ − 1} to the vertices of G such that the adjacent vertices receive values which differ by at least k, vertices connected by a path of length two receive values which differ by at… (More)

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