## 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 vert f(x) - f(y)\vert ≥ 2 if d(x,y) = 1 and vert 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\in V(G) = k. In this paper, we develop a dramatically new approach on the analysis of the adjacency matrices of the graphs to estimate the upper bounds of λ-numbers of the four standard graph products. By the new approach, we can achieve more accurate results and with significant improvement of the previous bounds.

Original language | English |
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Pages (from-to) | 802-805 |

Number of pages | 4 |

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

Volume | 55 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2008 |

## Scopus Subject Areas

- Electrical and Electronic Engineering

## User-Defined Keywords

- Cartesian product
- Channel assignment
- Direct product
- L(2,1)-labeling
- Lexicographic product
- Strong product