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...

Tree-growth-climate relationships are usually assumed to have a stationary character, i.e., continuous and/or time-independent, along the lifetime of trees. The fact that non-stationarity, discontinuous time-variable, is more likely actually be their general rule, has been often neglected in dendrochronology. Nine silver fir, black pine and Scots residual ring-width index chronologies (RWIresid...

We consider the design of adaptive data structures for searching elements a tree-structured space. use natural generalization rotation-based online binary search tree model in which underlying space is set vertices tree. This based on simple structure decomposing graphs, previously known under several names including elimination trees, vertex rankings, and tubings. The equivalent to classical e...

Residual stresses have become an important player in the field of the structural integrity for many years. Having an exact knowledge of residual stress distributions can be essential in designing the engineering components as unexpected failures are inevitable where such stresses are ignored.  There are many residual stresses measurement techniques including destructive and non-destructive ones...