Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Labeling Chordal Graphs: Distance Two Condition
SIAM Journal on Discrete Mathematics
Trivalent Cayley graphs for interconnection networks
Information Processing Letters
On the $\lambda$-Number of $Q_n$ and Related Graphs
SIAM Journal on Discrete Mathematics
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
A new 3D representation of trivalent Cayley networks
Information Processing Letters
The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
Labeling Products of Complete Graphs with a Condition at Distance Two
SIAM Journal on Discrete Mathematics
Labeling trees with a condition at distance two
Discrete Mathematics
Coloring Powers of Planar Graphs
SIAM Journal on Discrete Mathematics
Efficient algorithms for checking the equivalence of multistage interconnection networks
Journal of Parallel and Distributed Computing
L(h,1)-labeling subclasses of planar graphs
Journal of Parallel and Distributed Computing
The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography
The Computer Journal
Discrete Applied Mathematics
Graph labeling and radio channel assignment
Journal of Graph Theory
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Given two non-negative integers h and k, an L(h, k)-labeling of a graph G = (V, E) is a function from the set V to a set of colors, such that adjacent nodes take colors at distance at least h, and nodes at distance 2 take colors at distance at least k. The aim of the L(h, k)-labeling problem is to minimize the greatest used color. Since the decisional version of this problem is NP-complete, it is important to investigate particular classes of graphs for which the problem can be efficiently solved. It is well known that the most common interconnection topologies, such as Butterfly-like, Beneš, CCC, Trivalent Cayley networks, are all characterized by a similar structure: they have nodes organized as a matrix and connections are divided into layers. So we naturally introduce a new class of graphs, called (l × n)-multistage graphs, containing the most common interconnection topologies, on which we study the L(h, k)-labeling. A general algorithm for L(h, k)-labeling these graphs is presented, and from this method an efficient L(2, 1)-labeling for Butterfly and CCC networks is derived. Finally we describe a possible generalization of our approach.