On Resonance Graphs of Catacondensed Hexagonal Graphs: Structure, Coding, and Hamilton Path Algorithm
نویسندگان
چکیده
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 canonical binary coding of 1-factors of catacondensed hexagonal graphs is also described. This coding together with the decomposition theorem leads to an algorithm that returns a Hamilton path of a catacondensed hexagonal graph. ————————————————— ∗Supported in part by the Ministry of Education, Science and Sport of Slovenia under the grant 0101-P504.
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