## Abstract

The frequency assignment problem is to assign a frequency which is a nonnegative integer to each radio transmitter so that interfering transmitters are assigned frequencies whose separation is not in a set of disallowed separations. This frequency assignment problem can be modelled with vertex labelings of graphs. An L(2,1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all nonnegative integers such that f(x) - f(y) \≥ 2 if d(x,y) = 1 and f(x) - f(y) ≥ 1 if d(x,y) = 2, where d(x,y) denotes the distance between x and y in G. The L(2,1)-labeling number λ(G) of G is the smallest number k such that G has an L(2,1)-labeling with max {f(v) : v ε V(G)} = k. This paper considers the graph formed by the direct product and the strong product of two graphs and gets better bounds than those of Klavžar and Špacapan with refined approaches.

Original language | English |
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Pages (from-to) | 685-689 |

Number of pages | 5 |

Journal | IEEE Transactions on Circuits and Systems II: Express Briefs |

Volume | 55 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2008 |

## Scopus Subject Areas

- Electrical and Electronic Engineering

## User-Defined Keywords

- Channel assignment
- Graph direct product
- Graph strong product
- L(2, 1) -labeling