Department of Mathematics
A new approach to the L(2,1) -labeling of some products of graphs
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. © 2008 IEEE.
Cartesian product, Channel assignment, Direct product, L(2, 1)-labeling, Lexicographic product, Strong product
Source Publication Title
IEEE Transactions on Circuits and Systems II: Express Briefs
Institute of Electrical and Electronics Engineers
Shiu, Wai Chee, Zhendong Shao, Kin Keung Poon, and David Zhang. "A new approach to the L(2,1) -labeling of some products of graphs." IEEE Transactions on Circuits and Systems II: Express Briefs 55.8 (2008): 802-805.