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
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
On L(d, 1)-labelings of graphs
Discrete Mathematics
Labeling Products of Complete Graphs with a Condition at Distance Two
SIAM Journal on Discrete Mathematics
A Theorem about the Channel Assignment Problem
SIAM Journal on Discrete Mathematics
Labeling Planar Graphs with Conditions on Girth and Distance Two
SIAM Journal on Discrete Mathematics
A bound on the chromatic number of the square of a planar graph
Journal of Combinatorial Theory Series B
Coloring the square of a planar graph
Journal of Graph Theory
(2,1)-Total labelling of outerplanar graphs
Discrete Applied Mathematics
Bounds for the L(d, 1): number of diameter 2 graphs, trees and cacti
International Journal of Mobile Network Design and Innovation
Labelling planar graphs without 4-cycles with a condition on distance two
Discrete Applied Mathematics
(2,1)-Total labelling of trees with sparse vertices of maximum degree
Information Processing Letters
(2,1)-Total number of trees with maximum degree three
Information Processing Letters
An O(n1.75) algorithm for L(2,1)-labeling of trees
Theoretical Computer Science
New upper bounds on the L(2,1)-labeling of the skew and converse skew product graphs
Theoretical Computer Science
| Hi-index | 0.05 |
An L(2, 1)-labelling of a graph G is an assignment of nonnegative integers to the vertices of G such that adjacent vertices have numbers at least 2 apart, and vertices at distance 2 have distinct numbers. The L (2, 1)-labelling number λ(G) of G is the minimum range of labels over all such labellings. It was shown by Griggs and Yeh [Labelling graphs with a condition at distance 2, SIAM J. Discrete Math. 5 (1992) 586-595] that every tree T has Δ + 1 ≤ λ(T)≤Δ + 2. This paper provides a sufficient condition for λ(T) = Δ + 1. Namely, we prove that if a tree T contains no two vertices of maximum degree at distance either 1, 2, or 4, then λ(T) = Δ + 1. Examples of trees T with two vertices of maximum degree at distance 4 such that λ(T) = Δ + 2 are constructed.