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
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
Labeling trees with a condition at distance two
Discrete Mathematics
Discrete Applied Mathematics
On the Structure of Graphs with Non-Surjective L(2,1)-Labelings
SIAM Journal on Discrete Mathematics
Graph labeling and radio channel assignment
Journal of Graph Theory
An extremal problem on non-full colorable graphs
Discrete Applied Mathematics
Note: On the hole index of L(2,1)-labelings of r-regular graphs
Discrete Applied Mathematics
On island sequences of labelings with a condition at distance two
Discrete Applied Mathematics
| Hi-index | 0.04 |
The λ-number of a graph G, denoted λ(G), is the smallest integer k such that there exists a function from V(G) into {0, 1, 2,..., k} under which adjacent vertices receive integers which differ by at least 2 and vertices at distance two receive integers which differ by at least 1. We establish the infinitude of the collection of connected graphs G with fixed maximum degree Δ ≥ 4 and fixed λ-number Δ + t, 1 ≤ t ≤ Δ - 1 such that no λ-labeling of G into {0, 1, 2,...., λ(G)} is surjective. Also, from among graphs with no surjective λ-labelings, we construct connected graphs with maximum degree 3, λ-number 5 and arbitrarily large order.