#### Document Type

Journal Article

#### Department/Unit

Department of Mathematics

#### Title

Improved bounds on the L(2,1) -number of direct and strong products of graphs

#### Language

English

#### 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. © 2008 IEEE.

#### Keywords

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

#### Publication Date

2008

#### Source Publication Title

IEEE Transactions on Circuits and Systems II: Express Briefs

#### Volume

55

#### Issue

7

#### Start Page

685

#### End Page

689

#### Publisher

Institute of Electrical and Electronics Engineers

#### DOI

10.1109/TCSII.2008.921411

#### Link to Publisher's Edition

#### ISSN (print)

15497747

#### Recommended Citation

Shao, Zhendong,
Sandi Klavžar,
Wai Chee Shiu,
and
David Zhang.
"Improved bounds on the L(2,1) -number of direct and strong products of graphs."
*IEEE Transactions on Circuits and Systems II: Express Briefs*
55.7
(2008): 685-689.