摘要
Some physicists depicted the molecular structure SnCl_2 · 2（H_2O） by a piece of an Archimedean tiling（4.8.8） that is a partial cube. Inspired by this fact, we determine Archimedean tilings whose connected subgraphs are all partial cubes. Actually there are only four Archimedean tilings,（4.4.4.4）,（6.6.6）,（4.8.8） and（4.6.12）, which have this property. Furthermore, we obtain analytical expressions for Wiener numbers of some connected subgraphs of（4.8.8） and（4.6.12） tilings. In addition, we also discuss their asymptotic behaviors.
Some physicists depicted the molecular structure SnCl_2 · 2（H_2O） by a piece of an Archimedean tiling（4.8.8） that is a partial cube. Inspired by this fact, we determine Archimedean tilings whose connected subgraphs are all partial cubes. Actually there are only four Archimedean tilings,（4.4.4.4）,（6.6.6）,（4.8.8） and（4.6.12）, which have this property. Furthermore, we obtain analytical expressions for Wiener numbers of some connected subgraphs of（4.8.8） and（4.6.12） tilings. In addition, we also discuss their asymptotic behaviors.
基金
Supported by the National Natural Science Foundation of China under Grant No.11471273 and No.11271307
Youth Research Fund Project of Chengyi College of Jimei University under Grant No.CK17007
