关于矩形和斜带模型的反强迫数和反凯库勒数  

On the Anti-Forcing Number and the Anti-Kekul Number of Rectangular and Skew Strip Models

作　　者：汤四平[1] 唐芬芳[2] 曹显兵[3] 

机构地区：[1]湖南科技大学数学与计算科学学院,湖南湘潭411201 [2]湖南师范大学数学与计算机科学学院,湖南长沙410081 [3]北京工商大学理学院,北京100048

出　　处：《数学的实践与认识》2012年第5期151-154,共4页Mathematics in Practice and Theory

基　　金：湖南省科技厅科技计划项目(2011FJ6093);北京市属高等学校人才强教计划(201102)

摘　　要：在苯类化合物的凯库勒结构的研究中引入了反强迫数和反凯库勒数.通过分析矩形和斜带模型苯类化合物的分子图的结构,证明了具有k行l列的矩形R[k,l]和斜带模型Z[k,l]的反凯库勒数是2,R[k,l]的反强迫数是l,Z[k,l]的反强迫数不超过[(l+1)/2],其中[x]表示不超过x的最大整数.The anti-forcing number and anti-Kekule number are introduced for studying Kekule structures in a benzenoid. The calculation of these invariants is demonstrated on rectangular models and skew strip models in this paper by analyzing the structures of their graphs, and it is shown that the anti-Kekule numbers of rectangular model R[k, l] and skew strip model Z[k, l] with k rows and l columns are 2, the anti-forcing number of R[k, l] is l and the anti-forcing number of Z[k, l] is not more than [2/1＋1] where [x] is the greatest integer no [2/1＋1] more than x.

关 键 词：反强迫数 反凯库勒数 凯库勒结构 矩形模型 斜带模型 

分 类 号：O156[理学—数学]