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An independent set with 108 vertices in the strong product of four 7-cycles (C7 2 C7 2 C7 2 C7) is given. This improves the best known lower bound for the Shannon capacity of the graph C7 which is the zero-error capacity of the corresponding noisy channel. The search was done by a computer program using the \simulated annealing" algorithm with a constant… (More)
The Fibonacci dimension fdim(G) of a graph G was introduced in  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)
In a wireless network, different devices are fitted with radio transmitters and receivers. The task of channel assignment problem is to assign radio frequencies to transmitters at different locations, without interference . The problem is closely related to graph labeling where the vertices of a graph represent the transmitters and the adjacencies show… (More)
An L(2,1)-labeling of a graph G = (V, E) is a function f from the vertex set V(G) to the set of nonnegative integers such that the labels on adjacent vertices differ by at least two and the labels on vertices at distance two differ by at least one. The span of f is the difference between the largest and the smallest numbers in f(V). The λ-number of G,… (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)