We introduce the minimum labelling spanning bi-connected subgraph problem (MLSBP) replacing connectivity by bi-connectivity in the well known minimum labelling spanning tree problem (MLSTP). A graph is bi-connected if, for every two vertices, there are, at least, two vertex-disjoint paths joining them. The problem consists in finding the spanning bi-connected subgraph or block with minimum set ...

We extend the de nition of edge-cordial graphs due to Ng and Lee for graphs on 4k, 4k+1, and 4k+3 vertices to include graphs on 4k+2 vertices, and show that, in fact, all graphs without isolated vertices are edge-cordial. Ng and Lee conjectured that all trees on 4k, 4k + 1, or 4k + 3 vertices are edge-cordial. Intuitively speaking, a graph G is said to be edge-cordial if its edges can be labell...

This paper introduces an approach for handling complex labelling problems driven by local constraints. The purpose is illustrated by two applications: detection of the road network on radar satellite images, and recognition of the cortical sulci on MRI images. Features must be initially extracted from the data to build a “feature graph” with structural relations. The goal is to endow each featu...

Suppose G is a finite graph with vertex-set V (G) and edge-set E(G). An edge-magic total labelling on G is a one-to-one map λ from V (G)∪E(G) onto the integers 1, 2, . . . , |V (G) ∪ E(G)| with the property that, given any edge (x, y), λ(x) + λ(x, y) + λ(y) = k for some constant k. Such a labelling is called strong if the smallest labels appear on the vertices. In this paper, we investigate the...

An infinite graph G is called dominating if its vertices can be labelled with natural numbers in such a way that for every function f : ω→ ω there is a ray in G whose sequence of labels eventually exceeds f . Conversely, G is called bounded if for every labelling of its vertices with natural numbers there exists a function f : ω→ω which eventually exceeds the labelling along any ray in G. This ...

A magic labelling of a graph G with sum s is the edges by nonnegative integers such that for each vertex v∈V, labels all incident to v equal same number s. Stanley gave remarkable results on labellings, but distinct case much more complicated. We consider complete construction labellings given G. The idea illustrated in detail dealing three regular graphs and non-regular graph. give combinatori...

A graph G is a difference graph iff there exists S ⊂ IN such that G is isomorphic to the graph DG(S) = (V,E), where V = S and E = {{i, j} : i, j ∈ V ∧ |i− j| ∈ V }. It is known that trees, cycles, complete graphs, the complete bipartite graphs Kn,n and Kn,n−1, pyramids and n-sided prisms (n ≥ 4) are difference graphs (cf. [4]). Giving a special labelling algorithm, we prove that cacti with a gi...

In this paper we address the problem of object recognition from 2D views. A new approach is proposed which combines the recognition systems based on Attribute Relational Graph matching (ARG)[2] and the Multimodal Neighbourhood signature (MNS) [7] method. In the new system we use the MNS method as a pre-matching stage to prune the number of model candidates. The ARG method then identifies the be...

When data are modeled as graphs, many research issues arise. In particular, there are many new challenges in query processing on graph data. This chapter studies the problem of structural queries on graph data. A hash-based structural join algorithm, HGJoin, is first proposed to handle reachability queries on graph data. Then, it is extended to the algorithms to process structural queries in fo...

The mod sum number p( G) of a connected graph G is the minimum number of isolated vertices required to transform G into a mod sum graph. It is known that the mod sum number is greater than zero for wheels, Wn, when n > 4 and for the complete graphs, Kn when n 2: 2. In this paper we show that p( Hm,n) > 0 for n > m ;::: 3. Vie show further that P(K2) = P(K3) = 1 while p(Kn) = n for n ;::: 4. We ...