In this paper, we deduce Wiener number of some connected subgraphs in tilings (4, 4, 4, 4) and (4, 6, 12), which are in Archimedean tilings. And compute their average distance.
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 sub...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.展开更多
文摘In this paper, we deduce Wiener number of some connected subgraphs in tilings (4, 4, 4, 4) and (4, 6, 12), which are in Archimedean tilings. And compute their average distance.
基金Supported by the National Natural Science Foundation of China under Grant No.11471273 and No.11271307Youth Research Fund Project of Chengyi College of Jimei University under Grant No.CK17007
文摘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.
