A mapping from the vertex set of a graph G = (V,E) into an interval of integers {0, . . . , k} is an L(2, 1)-labelling of G of span k if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common neighbour are mapped onto distinct integers. It is known that for any fixed k ≥ 4, deciding the existence of such a labelling is an NP-complete p...

Let G(V, E) be a graph with pvertices and qedges. f∶ V (G) → {0,1,2,…, p-1} bijection such that the induced function f*: E(G) N defined by f_sqdp* (uv)=|[f(u) ]2-[f(v) ]2 | for everyuv∈E(G).If is injective, then f_sqdp*is calledsquare difference labeling of G.A Gwhich admits square called graph. The greatest common incidence number (gcin) vertex v degree > 1 as divisor (g.c.d) labels inciden...

A graph G = (V, E) is said to be magic if there exists an integer labeling f : V ∪ E −→ [1, |V ∪ E|] such that f(x) + f(y) + f(xy) is constant for all edges xy ∈ E. Enomoto, Masuda and Nakamigawa proved that there are magic graphs of order at most 3n + o(n) which contain a complete graph of order n. Bounds on Sidon sets show that the order of such a graph is at least n + o(n). We close the gap ...

In this paper, we present a case study of predicting topics of scientific papers using a co-authorship graph. Co-authorship graphs constitute a specific view on bibliographic data, where scientific publications are modelled as a graph’s nodes, and two nodes are linked by an undirected edge whenever the two corresponding papers share at least one author. We apply a simple collective classificati...

We propose a new approach to querying graph databases. Our balances competing goals of expressive power, language clarity and computational complexity. A distinctive feature our is the ability express properties minimal (e.g. shortest) maximal most valuable) paths satisfying given criteria. To complex in modular way, we introduce labelling-generating ontologies. The resulting formalism computat...

Fraigniaud et al. (2006) introduced a new measure of difficulty for a distributed task in a network. The smallest number of bits of advice of a distributed problem is the smallest number of bits of information that has to be available to nodes in order to accomplish the task efficiently. Our paper deals with the number of bits of advice required to perform efficiently the graph searching proble...

Given a digraph (directed graph) with a labeling on its arcs, we study the problem of finding the Eulerian circuit of lexicographically minimum label. We prove that this problem is NP-complete in general, but if the labelling is locally injective (arcs going out from each vertex have different labels), we prove that it is solvable in linear time by giving an algorithm that constructs this circu...

We present an algorithm for checking whether an innnite transition system, deened by a graph grammar of a restricted kind, is a model of a formula of the temporal logic CTL. We rst present the syntax and the semantics of CTL, that are deened with respect to transition systems, labelled with atomic propositions. Then, we show how to adapt the formalism of graph grammars, for expressing such innn...

In this paper, we propose a semi-supervised online graph labelling method that a↵ords early learning capability. We use mean field approximation for predicting the unknown labels of the vertices of the graph with high accuracy on the standard benchmark datasets. The minimum cut is the energy function of our probabilistic model that encodes the uncertainty about the labels of the vertices. Our m...

We introduce a method for automatically labelling edges of word co-occurrence graphs with semantic relations. Therefore we only make use of training data already contained within the graph. Starting point of this work is a graph based on word co-occurrence of the German language, which is created by applying iterated co-occurrence analysis. The edges of the graph have been partially annotated b...