We use graceful labellings of paths to give a new way of constructing terraces for cyclic groups. These terraces are then used to find cyclic solutions to the three table Oberwolfach problem, OP(r, r, s), where two of the tables have equal size. In particular we show that, for every odd r ≥ 3 and even r with 4 ≤ r ≤ 16, there is a number Nr such that there is a cyclic solution to OP(r, r, s) wh...

We introduce a generalization of the well known concept of a graceful labeling. Given a graph Γ with e = d · m edges, we call d-graceful labeling of Γ an injective function from(m + 1)}. In the case of d = 1 and of d = e we find the classical notion of a graceful labeling and of an odd graceful labeling, respectively. Also, we call d-graceful α-labeling of a bipartite graph Γ a d-graceful label...

A symmetric group action on the maximal chains in a finite, ranked poset is local if the adjacent transpositions act in such a way that (i, i+ 1) sends each maximal chain either to itself or to one differing only at rank i. We prove that when Sn acts locally on a lattice, each orbit considered as a subposet is a product of chains. We also show that all posets with local actions induced by label...

To minimize the access cost in large disk arrays (RAID) Cohen et al. [5–7] introduced (d, f)-cluttered orderings of various set systems, d, f ∈ N. In case of a graph this amounts to an ordering of the edge set such that the number of points contained in any d consecutive edges is bounded by the number f . For the complete graph, Cohen et al. gave some optimal solution for small parameters d [5]...

For $G$ a simple, connected graph, vertex labeling $f:V(G)\to \Z_+$ is called \emph{radio of $G$} if it satisfies $|f(u)-f(v)|\geq\diam(G)+1-d(u,v)$ for all distinct vertices $u,v\in V(G)$. The number the minimal span over radio labelings $G$. If bijective onto $\{1,2,\dots,|V(G)|\}$ exists, graceful} graph. We determine diameter 3 Hamming graphs and show that an infinite subset them graceful.

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...

Graph labellings have been a very fruitful area of research in the last four decades. However, despite the staggering number of papers published in the field (over 1000), few general results are available, and most papers deal with particular classes of graphs and methods. Here we approach the problem from the computational viewpoint, and in a quite general way. We present the existence problem...

A rooted tree with diameter D is said to have an even degree sequence if every vertex has even degree except for one root and the leaves, which are in the last level D/2 . The degree sequence is said to be quasi even if every vertex has even degree except for one root, every vertex in level D/2 − 1 and the leaves, which are in the last level D/2 . Hrnčiar and Haviar [P. Hrnčiar, A. Haviar, All ...