Linear and cyclic radio k-labelings of trees

Mustapha Kchikech ; Riadh Khennoufa ; Olivier Togni

Discussiones Mathematicae Graph Theory, Tome 27 (2007), p. 105-123 / Harvested from The Polish Digital Mathematics Library

Résumé

Motivated by problems in radio channel assignments, we consider radio k-labelings of graphs. For a connected graph G and an integer k ≥ 1, a linear radio k-labeling of G is an assignment f of nonnegative integers to the vertices of G such that $|f(x)-f(y)| ≥ k+1-d_G(x,y)$, for any two distinct vertices x and y, where $d_G(x,y)$ is the distance between x and y in G. A cyclic k-labeling of G is defined analogously by using the cyclic metric on the labels. In both cases, we are interested in minimizing the span of the labeling. The linear (cyclic, respectively) radio k-labeling number of G is the minimum span of a linear (cyclic, respectively) radio k-labeling of G. In this paper, linear and cyclic radio k-labeling numbers of paths, stars and trees are studied. For the path Pₙ of order n ≤ k+1, we completely determine the cyclic and linear radio k-labeling numbers. For 1 ≤ k ≤ n-2, a new improved lower bound for the linear radio k-labeling number is presented. Moreover, we give the exact value of the linear radio k-labeling number of stars and we present an upper bound for the linear radio k-labeling number of trees.

Détail

Publié le : 2007-01-01

Zbl 1137.05063

EUDML-ID : urn:eudml:doc:270675

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