Binary coding of resonance graphs of catacondensed polyhexesVesel, Aleksander (Avtor) graphsgraph theoryresonance graphsA catacondensed polyhex H is a connected subgraph of a hexagonal system such that any edge of H lies in a hexagon of H, any triple of hexagons of H has an empty intersection and the inner dual of H is a cactus graph. A perfect matching M of a catacondensed polyhex H is relevant if every cycle of the inner dual of H admitsa vertex that corresponds to the hexagon which contributes three edges in M. The vertex set of the graph R˜(H) consists of all relevant perfect matchings of H, two perfect matchings being adjacent whenever their symmetric difference forms the edge set of a hexagon of H. A labeling that assigns in linear time a binary string to every relevant perfect matching of a catacondensed polyhex is presented. The introduced labeling defines an isometric embedding of R˜(H) into a hypercube.Faculty of Science & University of Kragujevac20232024-04-10 03:50:27Članek v reviji88140sl