Let r be a nonnegative integer. The r-Lee sphere inRn centred on 0 of major axis E e1, . . . , E en is the set of n-cubes C(Y ) where d(0, Y ) ≤ r and Y has integer coordinates. More generally, an r… (More)

Consider a finite family of n circular disks, each of diameter one, whose interiors are pair-wise disjoint and contained in a square S. A classical problem is to find the smallest side s of such a… (More)

In the language of mathematical chemistry, Fibonacci cubes can be defined as the resonance graphs of fibonacenes. Lucas cubes form a symmetrization of Fibonacci cubes and appear as resonance graphs… (More)

Let Γn and Λn be the n-dimensional Fibonacci cube and Lucas cube, respectively. The domination number γ of Fibonacci cubes and Lucas cubes is studied. In particular it is proved that γ(Λn) is bounded… (More)

B. D. Acharya [I] has introduced the notion of set-graceful graphs, a set analog of the well known graceful numbering of graphs. Following this author, a set-indexer of a graph G = (V, E) is an… (More)

We introduce and study a common generalization of 1-error binary perfect codes and perfect single error correcting codes in Lee metric, namely perfect codes on products of paths of length 2 and of… (More)

The λ-number of a graph G is the minimum value λ such that G admits a labeling with labels from {0, 1, . . . , λ} where vertices at distance two get different labels and adjacent vertices get labels… (More)

The Fibonacci cube of dimension n, denoted as Γn, is the subgraph of n-cube Qn induced by vertices with no consecutive 1’s. We study the maximum number of disjoint subgraphs in Γn isomorphic to Qk,… (More)