L(2,1)-labeling of direct product of paths and cycles

Authors:
Pranava K. Jha;Sandi Klavar;Aleksander Vesel
Affiliations:
Department of Computer Science, St. Cloud State University, St. Cloud, MN 56301, USA;Department of Mathematics and Computer Science, PeF, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia;Department of Mathematics and Computer Science, PeF, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
Venue:
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Year:
2005

Citing 19
Cited 2

The matching polynomial of a polygraph

Discrete Applied Mathematics
A randomised 3-colouring algorithm

Discrete Mathematics - Graph colouring and variations
T-colorings of graphs: recent results and open problems

Discrete Mathematics - Special issue: advances in graph labelling
Labelling graphs with a condition at distance 2

SIAM Journal on Discrete Mathematics
Labeling Chordal Graphs: Distance Two Condition

SIAM Journal on Discrete Mathematics
Relating path coverings to vertex labellings with a condition at distance two

Discrete Mathematics
On the $\lambda$-Number of $Q_n$ and Related Graphs

SIAM Journal on Discrete Mathematics
On the size of graphs labeled with condition at distance two

Journal of Graph Theory
The $L(2,1)$-Labeling Problem on Graphs

SIAM Journal on Discrete Mathematics
Analysis of the mean field annealing algorithm for graph colouring

Journal of Artificial Neural Networks - Special issue: neural networks for optimization
Algebraic approach to fasciagraphs and rotagraphs

Discrete Applied Mathematics
Distance-related invariants on polygraphs

Discrete Applied Mathematics - Special issue: 50th anniversary of the Wiener index
Fixed parameter complexity of λ-labelings

Discrete Applied Mathematics - special issue on the 25th international workshop on graph theoretic concepts in computer science (WG'99)
Improved lower bound on the Shannon capacity of C7

Information Processing Letters
Smallest independent dominating sets in Kronecker products of cycles

Discrete Applied Mathematics
Labeling Products of Complete Graphs with a Condition at Distance Two

SIAM Journal on Discrete Mathematics
Diagonal and Toroidal Mesh Networks

IEEE Transactions on Computers
Computing graph invariants on rotagraphs using dynamic algorithm approach: the case of (2,1)-colorings and independence numbers

Discrete Applied Mathematics
Graph labeling and radio channel assignment

Journal of Graph Theory

L(2,1)-labelings of the edge-path-replacement of a graph

Journal of Combinatorial Optimization
L(d,1)-labelings of the edge-path-replacement of a graph

Journal of Combinatorial Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

An L(2,1)-labeling of a graph G is an assignment of labels from {0,1,...,@l} to the vertices of G such that vertices at distance two get different labels and adjacent vertices get labels that are at least two apart. The @l-number @l(G) of G is the minimum value @l such that G admits an L(2,1)-labeling. Let GxH denote the direct product of G and H. We compute the @l-numbers for each of C"7"ixC"7"j, C"1"1"ixC"1"1"jxC"1"1"k, P"4xC"m, and P"5xC"m. We also show that for n=6 and m=7, @l(P"nxC"m)=6 if and only if m=7k, k=1. The results are partially obtained by a computer search.