A hypergraph H is a sum hypergraph iff there are a finite S ⊆ IN and d, d ∈ IN with 1 < d ≤ d such that H is isomorphic to the hypergraph Hd,d(S) = (V, E) where V = S and E = {e ⊆ S : d ≤ |e| ≤ d ∧ v∈e v ∈ S}. For an arbitrary hypergraph H the sum number σ = σ(H) is defined to be the minimum number of isolated vertices y1, . . . , yσ 6∈ V such that H ∪ {y1, . . . , yσ} is a sum hypergraph. Gene...

Given a graph G with n vertices and an Abelian group A of order n, an A-distance antimagic labelling of G is a bijection from V (G) to A such that the vertices of G have pairwise distinct weights, where the weight of a vertex is the sum (under the operation of A) of the labels assigned to its neighbours. An A-distance magic labelling of G is a bijection from V (G) to A such that the weights of ...

This paper presents a meta-algorithm for the computation of preferred labellings, based on the general recursive schema for argumentation semantics called SCC-Recursiveness. The idea is to recursively decompose a framework so as to compute semantics labellings on restricted sub-frameworks, in order to reduce the computational effort. The meta-algorithm can be instantiated with a specific “base ...

This paper presents a meta-algorithm for the computation of preferred labellings, based on the general recursive schema for argumentation semantics called SCC-Recursiveness. The idea is to recursively decompose a framework so as to compute semantics labellings on restricted sub-frameworks, in order to reduce the computational effort. The meta-algorithm can be instantiated with a specific “base ...

In 1994, Du and Sun conjectured that, for any positive even n and any integer m, the digraph n. −→ Cm is graceful. In this paper we prove the conjecture. Also, in 1985, Bloom and Hsu mentioned that the question remains open for the non generalized graceful labelings. For example, the following question is currently unanswered: How many distinct graceful labelings does a designated graceful digr...

We initially describe a feature-rich discriminative Conditional Random Field (CRF) model for Information Extraction in the workshop announcements domain, which offers good baseline performance in the PASCAL shared task. We then propose a method for leveraging domain knowledge in Information Extraction tasks, scoring candidate document labellings as one-value-per-field templates according to dom...

A (d, 1)-total labelling of a graph G assigns integers to the vertices and edges of G such that adjacent vertices receive distinct labels, adjacent edges receive distinct labels, and a vertex and its incident edges receive labels that differ in absolute value by at least d. The span of a (d, 1)-total labelling is the maximum difference between two labels. The (d, 1)-total number, denoted λTd (G...

One of the most famous open problems in graph theory is the Graceful Tree Conjecture, which states that every finite tree has a graceful labeling. In this paper, we define graceful labelings for countably infinite graphs, and state and verify a Graceful Tree Conjecture for countably infinite trees.

In this paper, we have identified some of the graceful graphs which are obtained from the amalgamations of two graceful graphs. A conjecture is also discussed for general graceful graphs and the same is proved for Fibonacci graceful graphs. Mathematics Subject Classification: 05C78

A p. q graph G = V,E is said to be a square graceful graph ifthere exists an injective function f: V G → 0,1,2,3,... , q such that the induced mapping fp : E G → 1,4,9,... , q 2 defined by fp uv = f u − f v is an injection. The function f is called a square graceful labeling of G. In this paper the square graceful labeling of the caterpillar S X1,X2 ,... ,Xn , the graphs Pn−1 1,2,...n ,mK1,n ∪ ...