Geodesic
L(2, 1)-Labeling of Circulant Graphs
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 1, pp. 143-155

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An L(2, 1)-labeling of a graph Γ is an assignment of non-negative integers to the vertices such that adjacent vertices receive labels that differ by at least 2, and those at a distance of two receive labels that differ by at least one. Let λ_2^1 (Γ) denote the least λ such that Γ admits an L(2, 1)-labeling using labels from { 0, 1, . . ., λ}. A Cayley graph of group G is called a circulant graph of order n, if G = ℤ_n. In this paper initially we investigate the upper bound for the span of the L(2, 1)-labeling for Cayley graphs on cyclic groups with “large” connection sets. Then we extend our observation and find the span of L(2, 1)-labeling for any circulants of order n.
Keywords: graph coloring, L(2, 1)-labeling, circulants 
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     title = {L(2, {1)-Labeling} of {Circulant} {Graphs}},
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Mitra, Sarbari; Bhoumik, Soumya. L(2, 1)-Labeling of Circulant Graphs. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 1, pp. 143-155. http://geodesic.mathdoc.fr/item/DMGT_2019_39_1_a11/