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
Labeling Products of Complete Graphs with a Condition at Distance Two
SIAM Journal on Discrete Mathematics
Real Number Graph Labellings with Distance Conditions
SIAM Journal on Discrete Mathematics
The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography
The Computer Journal
Real Number Channel Assignments for Lattices
SIAM Journal on Discrete Mathematics
Bounds for the Real Number Graph Labellings and Application to Labellings of the Triangular Lattice
SIAM Journal on Discrete Mathematics
Graph labellings with variable weights, a survey
Discrete Applied Mathematics
Labeling the r-path with a condition at distance two
Discrete Applied Mathematics
Optimal Real Number Graph Labellings of a Subfamily of Kneser Graphs
SIAM Journal on Discrete Mathematics
| Hi-index | 0.04 |
For non-negative real x"0 and simple graph G, @l"x"""0","1(G) is the minimum span over all labelings that assign real numbers to the vertices of G such that adjacent vertices receive labels that differ by at least x"0 and vertices at distance two receive labels that differ by at least 1. In this paper, we introduce the concept of @l-invertibility: G is @l-invertible if and only if for all positive x, @l"x","1(G)=x@l"1"x","1(G^c). We explore the conditions under which a graph is @l-invertible, and apply the results to the calculation of the function @l"x","1(G) for certain @l-invertible graphs G. We give families of @l-invertible graphs, including certain Kneser graphs, line graphs of complete multipartite graphs, and self-complementary graphs. We also derive the complete list of all @l-invertible graphs with maximum degree 3.