Introduction to finite fields and their applications
Introduction to finite fields and their applications
Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
On the $\lambda$-Number of $Q_n$ and Related Graphs
SIAM Journal on Discrete Mathematics
A coloring problem on the n-cube
Discrete Applied Mathematics
Coloring Hamming graphs, optimal binary codes, and the 0/1-Borsuk problem in low dimensions
Computational Discrete Mathematics
Labeling Products of Complete Graphs with a Condition at Distance Two
SIAM Journal on Discrete Mathematics
New bounds on a hypercube coloring problem
Information Processing Letters
A channel assignment problem for optical networks modelled by Cayley graphs
Theoretical Computer Science
On a hypercube coloring problem
Journal of Combinatorial Theory Series A
Labelling Cayley Graphs on Abelian Groups
SIAM Journal on Discrete Mathematics
The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography
The Computer Journal
Graph labeling and radio channel assignment
Journal of Graph Theory
Optimal radio labellings of complete m-ary trees
Discrete Applied Mathematics
The L(h,1,1)-labelling problem for trees
European Journal of Combinatorics
Distance three labelings of trees
Discrete Applied Mathematics
Graph coloring with cardinality constraints on the neighborhoods
Discrete Optimization
New results on two hypercube coloring problems
Discrete Applied Mathematics
| Hi-index | 0.04 |
Let i"1=i"2=i"3=1 be integers. An L(i"1,i"2,i"3)-labelling of a graph G=(V,E) is a mapping @f:V-{0,1,2,...} such that |@f(u)-@f(v)|=i"t for any u,v@?V with d(u,v)=t, t=1,2,3, where d(u,v) is the distance in G between u and v. The integer @f(v) is called the label assigned to v under @f, and the difference between the largest and the smallest labels is called the span of @f. The problem of finding the minimum span, @l"i"""1","i"""2","i"""3(G), over all L(i"1,i"2,i"3)-labellings of G arose from channel assignment in cellular communication systems, and the related problem of finding the minimum number of labels used in an L(i"1,i"2,i"3)-labelling was originated from recent studies on the scalability of optical networks. In this paper we study the L(i"1,i"2,i"3)-labelling problem for hypercubes Q"d (d=3) and obtain upper and lower bounds on @l"i"""1","i"""2","i"""3(Q"d) for any (i"1,i"2,i"3).