The problem of finding a graceful labelling of a graph, or proving that the graph is not graceful, has previously been modelled as a CSP. A new and much faster CSP model of the problem is presented, with several new results for graphs whose gracefulness was previously unknown. Several classes of graph that are conjectured to be graceful only for small instances are investigated: after a certain...

A gracious labelling g of a tree is a graceful labelling in which, treating the tree as a bipartite graph, the label of any edge (d,u) (d a ‘down’ and u an ‘up’ vertex) is g(u) – g(d). A gracious k-labelling is one such that each residue class modulo k has the ‘correct’ numbers of vertex and edge labels that is, the numbers that arise by interpreting the labels of a gracious labelling modulo k....

Huge and expensive computation resources are usually required to perform graph labelling at high speed. This fact restricts an extensive use of this methodology in industrial applications such as visual inspection. A new systolic architecture is presented which computes structural distances between cliques of different graphs based on a modified incremental Levenshtein distance algorithm. The d...

Given any fixed non-negative integer values h and k, the L(h, k)-labelling problem consists in an assignment of non-negative integers to the nodes of a graph such that adjacent nodes receive values which differ by at least h, and nodes connected by a 2 length path receive values which differ by at least k. The span of an L(h, k)-labelling is the difference between the largest and the smallest a...

The context of this paper, already presented at ICDAR 2015, is the labelling of a document image database in an industrial process. Our work focuses on the quality assessment of a given labelled database. In most practical cases, a database is manually labelled by an operator who has to browse sequentially the images (presented as thumbnails) until the whole database is labelled. This task is v...

A sum graph G is a graph with a mapping of the vertex set of G onto a set of positive integers S in such a way that two vertices of G are adjacent if and only if the sum of their labels is an element of S. In an exclusive sum graph the integers of S that are the sum of two other integers of S form a set of integers that label a collection of isolated vertices associated with the graph G. A grap...

background: ubi 29-41 (a derivative of antimicrobial peptide ubiquicidin) labelled with 99mtc is reported to discriminate between bacterial infections and sterile inflammatory processes. in this study, three lyophilized kit were performed, one of them based on the direct labelling with only sncl2 as reducing agent , and other two based on 6- hydrazinopyridine-3-carboxylic acid (hynic) and trici...

In this paper the researcher prepares truth table for labeling of Bloom Torus graph by admitting condition Smarandachely product cordial labelling. on is such a with induced

This paper introduces an unsupervised graph-based method that selects textual labels for automatically generated topics. Our approach uses the topic keywords to query a search engine and generate a graph from the words contained in the results. PageRank is then used to weigh the words in the graph and score the candidate labels. The state-of-the-art method for this task is supervised (Lau et al...