Partial Cubes and Archimedean Tilings  

作　　者：Yun-jing PAN Ming-fang XIE Fu-ji ZHANG 

机构地区：[1]ChengYi College, Jimei University, Xiamen 361021, China [2]Jiangxia University, Fuzhou 350108, China [3]School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

出　　处：《Acta Mathematicae Applicatae Sinica》2018年第4期782-791,共10页应用数学学报（英文版）

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

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.

关 键 词：archimedean tiling wiener number partial cube average distance 

分 类 号：O157.5[理学—数学]