
The Space Complexity of Sum Labelling
A graph is called a sum graph if its vertices can be labelled by distinc...
read it

Adjacency Labelling for Planar Graphs (and Beyond)
We show that there exists an adjacency labelling scheme for planar graph...
read it

Distinguishing numbers and distinguishing indices of oriented graphs
A distinguishing rvertexlabelling (resp. redgelabelling) of an undir...
read it

Optimal labelling schemes for adjacency, comparability and reachability
We construct asymptotically optimal adjacency labelling schemes for ever...
read it

Minimum Labelling biConnectivity
A labelled, undirected graph is a graph whose edges have assigned labels...
read it

Local certification of graphs on surfaces
A proof labelling scheme for a graph class 𝒞 is an assignment of certifi...
read it

On the Relation Between the Common Labelling and the Median Graph
In structural pattern recognition, given a set of graphs, the computatio...
read it
Graphs without gapvertexlabellings: families and bounds
A proper labelling of a graph G is a pair (π,c_π) in which π is an assignment of numeric labels to some elements of G, and c_π is a colouring induced by π through some mathematical function over the set of labelled elements. In this work, we consider gapvertexlabellings, in which the colour of a vertex is determined by a function considering the largest difference between the labels assigned to its neighbours. We present the first upperbound for the vertexgap number of arbitrary graphs, which is the least number of labels required to properly label a graph. We investigate families of graphs which do not admit any gapvertexlabelling, regardless of the number of labels. Furthermore, we introduce a novel parameter associated with this labelling and provide bounds for it for complete graphs K_n.
READ FULL TEXT
Comments
There are no comments yet.