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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 Γ d , 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)

An algorithm is described by means of which the Kekulé structures of a catacondensed benzenoid molecule (with h hexagons) are transformed into binary codes (of length h). By this, computer-aided manipulations with, and memory-storage of Kekulé structures are much facilitated. Any Kekulé structure can easily be recovered from its binary code.

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)

- Sandi Klavžar, Aleksander Vesel, Petražigert
- 2010

The vertex set of the resonance graph of a hexagonal graph G consists of 1-factors of G, two 1-factors being adjacent whenever their symmetric difference forms the edge set of a hexagon of G. A decomposition theorem for the resonance graphs of catacondensed hexagonal graph is proved. The theorem intrinsically uses the Cartesian product of graphs. A… (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)