# Aleksander Vesel

• Discrete Applied Mathematics
• 2003
Rotagraphs generalize all standard products of graphs in which one factor is a cycle. A computer based approach for searching graph invariants on rotagraphs is proposed and two of its applications are presented. First, the-numbers of the Cartesian product of a cycle and a path are computed, where the-number of a graph G is the minimum number of colors(More)
• Algorithmica
• 2007
Fibonacci cubes are induced subgraphs of hypercubes based on Fibonacci strings. They were introduced to represent interconnection networks as an alternative to the hypercube networks. We derive a characterization of Fibonacci cubes founded on the concept of resonance graphs. The characterization is the basis for an algorithm which recognizes these graphs in(More)
• 1
• The Fibonacci dimension fdim(G) of a graph G was introduced in [1] as the smallest integer d such that G admits an isometric embedding into Γd, the d-dimensional Fibonacci cube. The Fibonacci dimension of the resonance graphs of catacondensed benzenoid systems is studied. This study is inspired by the fact, that the Fibonacci cubes are precisely the(More)
Combinatorial optimization problems arise in situations where discrete choices must be made and solving them amounts to finding an optimal solution among a finite or countably infinite number of alternatives. Optimality relates to some cost criterion, which provides a quantitative measure of the quality of each solution. This area of discrete mathematics is(More)
Fibonacci strings are binary strings that contain no two consecutive 1s. The Fibonacci cube Γ h is the subgraph of the h-cube induced by the Fibonacci strings. These graphs are applicable as interconnection networks and in theoretical chemistry, and lead to the Fibonacci dimension of a graph. We derive a new characterization of Fibonacci cubes. The(More)
• 7
• Discrete Applied Mathematics
• 2005
An L(d,1)-labeling of a graph G is an assignment of nonnegative integers to the vertices such that adjacent vertices receive labels that differ by at least d and those at a distance of two receive labels that differ by at least one, where d 1. Let d1 (G) denote the least such that G admits an L(d,1)-labeling using labels from {0, 1, . . . , }. We prove that(More)