Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Multichromatic numbers, star chromatic numbers and Kneser graphs
Journal of Graph Theory
Hamiltonicity and circular distance two labellings
Discrete Mathematics
Optimal Channel Assignments for Lattices with Conditions at Distance Two
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 12 - Volume 13
New bounds for the L(h, k) number of regular grids
International Journal of Mobile Network Design and Innovation
Graph labeling and radio channel assignment
Journal of Graph Theory
Multi-coloring the Mycielskian of graphs
Journal of Graph Theory
The Computer Journal
On n-fold L(j,k)-and circular L(j,k)-labelings of graphs
Discrete Applied Mathematics
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Let n,j,k be nonnegative integers. An n-fold L(j,k)-labeling of a graph G is an assignment f of sets of nonnegative integers of order n to the vertices of G such that, for any two vertices u,v and any two integers a驴f(u), b驴f(v), |a驴b|驴j if uv驴E(G), and |a驴b|驴k if u and v are distance two apart. The span of f is the absolute difference between the maximum and minimum integers used by f. The n-fold L(j,k)-labeling number of G is the minimum span over all n-fold L(j,k)-labelings of G.Let n,j,k and m be nonnegative integers. An n-fold circular m-L(j,k)-labeling of a graph G is an assignment f of subsets of {0,1,驴,m驴1} of order n to the vertices of G such that, for any two vertices u,v and any two integers a驴f(u), b驴f(v), min{|a驴b|,m驴|a驴b|}驴j if uv驴E(G), and min{|a驴b|,m驴|a驴b|}驴k if u and v are distance two apart. The minimum m such that G has an n-fold circular m-L(j,k)-labeling is called the n-fold circular L(j,k)-labeling number of G.This paper provides upper and lower bounds for the n-fold L(j,1)-labeling number and the n-fold circular L(j,1)-labeling number of the triangular lattice and determines the n-fold L(2,1)-labeling number and n-fold circular L(2,1)-labeling number of the triangular lattice for n驴3.