T-colorings of graphs: recent results and open problems
Discrete Mathematics - Special issue: advances in graph labelling
Labelling graphs with a condition at distance 2
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
Smallest independent dominating sets in Kronecker products of cycles
Discrete Applied Mathematics
Labeling Products of Complete Graphs with a Condition at Distance Two
SIAM Journal on Discrete Mathematics
L(2, 1)-labelings of Cartesian products of two cycles
Discrete Applied Mathematics
The minimum span of L(2,1)-labelings of certain generalized Petersen graphs
Discrete Applied Mathematics
| Hi-index | 0.04 |
An L(d,1)-labeling of a graph G is an assignment of nonnegative integers to the vertices such that adjacent vertices receive labels that differ by at least d and those at a distance of two receive labels that differ by at least one, where d ≥ 1. Let λ1d(G) denote the least λ such that G admits an L(d,1)-labeling using labels from {0, 1, ..., λ}. We prove that (i) if d ≥ 1, k ≥ 2 and m0, ..., mk-1 are each a multiple of 2k + 2d - 1, then λ1d(Cm0 × ... × Cmk-1) ≤ 2k + 2d - 2, with equality if 1 ≤ d ≤ 2k, and (ii) if d ≥ 1, k ≥ 1 and m0, ..., mk-1 are each a multiple of 2k + 2d - 1, then λ1d (Cm0□ ...□Cmk-1) ≤ 2k + 2d - 2, with equality if 1 ≤ d ≤ 2k.