α-Labelings and the Structure of Trees with Nonzero α-Deficit

Constructing Graceful Graphs with Caterpillars

A graceful labeling of a graph G of size n is an injective assignment of integers from {0, 1,..., n} to the vertices of G, such that when each edge of G has assigned a weight, given by the absolute dierence of the labels of its end vertices, the set of weights is {1, 2,..., n}. If a graceful labeling f of a bipartite graph G assigns the smaller labels to one of the two stable sets of G, then f ...

Trees with Α-labelings and decompositions of complete graphs into non-symmetric isomorphic spanning trees

We examine constructions of non-symmetric trees with a flexible q-labeling or an α-like labeling, which allow factorization of K2n into spanning trees, arising from the trees with α-labelings.

A new application of the ⊗h-product to α-labelings

The weak tensor product was introduced by Snevily as a way to construct new graphs that admit α-labelings from a pair of known α-graphs. In this article, we show that this product and the application to α-labelings can be generalized by considering as a second factor of the product, a family Γ of bipartite (p, q)-graphs, p and q fixed. The only additional restriction that we should consider is ...

Non-zero probability of nearest neighbor searching

Nearest Neighbor (NN) searching is a challenging problem in data management and has been widely studied in data mining, pattern recognition and computational geometry. The goal of NN searching is efficiently reporting the nearest data to a given object as a query. In most of the studies both the data and query are assumed to be precise, however, due to the real applications of NN searching, suc...

Vertex Equitable Labelings of Transformed Trees